Stat Assistant Professor

With your perfect 4.0 from your undergrad, I anticipate that you will be admitted to every Statistics MS program you apply to. It's no big deal if you have been out of school for awhile. However, before you start your program, make sure to review Calculus I-III (you can skip any derivatives/integrals dealing with trigonometry, washer/disk methods, polar coordinates, arc length, and curvature) and maybe some linear algebra.
The main things you need to review from Calc I-III are differentiation and integration, including things like the chain rule, u-substitution, integration by parts, partial derivatives, and multiple integration.

Having those types of connections may indeed be helpful. It could also depend on who is on the admissions committee.
It just seems as though most of the "top" Statistics PhD programs are extremely selective about what domestic applicants they admit (to the point that some schools like Harvard and UPenn only have 1-3 domestic students enrolling each year). Some top programs like UC Berkeley, University of Washington, and Duke are a bit more flexible (in that they admit more Americans and not all from very prestigious undergrads).

Not nearly as important as the letters for Stat PhD programs. Since most Masters programs are unfunded, they will admit most students who meet the minimum coursework, GPA, and general GRE requirements.

I still think the likes of Columbia and Chicago might be tough. There was a combined Bachelor's/Master's American student at the school where I got my PhD from (a large flagship state university) who had done legitimate research on theoretical probability, had taken basically the entire Statistics PhD curriculum *and* a bunch of math PhD classes (measure theory, functional analysis, etc.), and he was still rejected from most of the top statistics PhD programs (he did end up at a very good program though -- one of the four "reaches" mentioned by the OP). I think the top schools are very competitive, and a sub-3.8 undergrad GPA from a less prestigious uni may have a more difficult time cracking schools like Columbia or Chicago. These schools don't accept many domestic students to begin with.
That said, the OP does have a very good profile, and I would encourage them to apply to more schools in the top 20 if they can afford it. 

With a 3.7+ from UC Berkeley and grades of B or better in your math/stat classes, I imagine you will not have any difficulty getting into most Statistics Masters programs. 

I think that it's a great idea to get a letter of recommendation from the person who supervised your first author paper. A first author paper is a clear sign of "research potential," even if it's not what you end up doing your dissertation research in. As long as your LOR writer can explain your research contribution in their recommendation letter and convey clearly that you performed statistical analysis, it should make a positive impression. 
I say go with the Epidemiology professor for a recommendation letter. Try to get at least one letter from a math professor who can highlight your mathematical abilities, your coursework in math, etc. 

Your profile looks pretty strong. I think Wisconsin, Penn State, UCLA, and Rice are definitely possible. Columbia, Michigan, UNC, and Washington might be slight reaches, as these are very competitive programs and there will be other domestic applicants to these programs who have better undergrad GPAs from more prestigious schools. However, your research experience is very solid, and your graduate school performance should instill enough confidence in your math abilities.
If I were you, I would apply to 4 schools in the range of Wisconsin to Rice and then pick two schools from Columbia, Michigan, UNC, and Washington to apply to (of those, I think Washington and UNC are more likely to admit you).

Oh, I was not aware of this at all. In any event, if the OP applies to programs at large state schools like TAMU, UMinnesota, etc., they might be able to get in. I have known people who got their PhDs from TAMU and UMN (and are now TT faculty at R1s) who did their undergrad at places like Central Michigan University or Southern Illinois University. I think **domestic** students from these regional schools with high GPAs stand a reasonable chance at most of the Stat PhD programs ranked 20-40 by USNWR.

I think your profile is good enough to get into UC Irvine. UCLA and UC Davis are also attainable for your profile.
I don't think top 30-60 is a reach at all, and you may even be able to get into some top 20 schools as well (big state schools like Iowa State and TAMU seem like a good bet -- and possibly University of Minnesota as well).
Consider taking one or two more upper division math classes this fall, and you should be good to go. 

Calculus I-III, Linear Algebra, and Real Analysis are the bare minimum you need for most Statistics PhD programs. However, more math beyond the bare minimum is always helpful in boosting your application. So strong performance in classes like abstract algebra, number theory, and complex analysis are definitely viewed positively by adcoms, as they signal mathematical maturity even if these subjects are not directly applicable to statistics. I would thus encourage you to take more math to boost your application. The only upper division statistics classes that are very helpful for Statistics PhDs are Calculus-based probability and statistical inference (at the undergrad level). These might make the first-year Casella & Berger mathematical statistics sequence somewhat easier. 
Some of the more "relevant" upper division math classes to Statistics are numerical analysis, advanced (proof-based) linear algebra, and optimization.  

For most Statistics or Biostatistics MS degrees, the most important things are, in order of importance:
 
1) Required coursework (Calc I-III and Linear Algebra), ideally with grades of B- or higher
2) GPA
3) GRE
4) everything else

If you are not interested in academia, then I don't see any reason not to graduate in four years if you can. The main advantages of taking a fifth (or sixth) year are:
- more time to find a job
- more time to get more publications on your CV. 
If you aren't interested in academia, then the second point is really moot. However, for those on this forum potentially interested in academic positions: if you have a good postdoc lined up in your fourth year, then I would still recommend finishing up more quickly, even if you don't have as many publications. The main consideration for taking an extra year is whether or not you will be much more competitive on the job market with that extra year. For example, I completed my PhD in four years, and by the time I graduated, I had only one publication and two papers submitted. However, I knew that if I stayed at my program a fifth year, I wouldn't have been able to make my CV significantly stronger, so I just graduated and went immediately to the postdoc.
Meanwhile, one of my classmates could have also graduated in four years just like me, but he stayed for the fifth year so he could get an Annals of Statistics paper accepted and on his CV. This ultimately put him in a much stronger position in the academic job market and he was able to get a TT job at a very good department. So in my classmate's case, it was definitely advantageous to take the fifth year to ensure his CV was stronger.

For most Statistics or Biostatistics MS degrees, the most important things are, in order of importance:
 
1) Required coursework (Calc I-III and Linear Algebra), ideally with grades of B- or higher
2) GPA
3) GRE
4) everything else

I think it is definitely less competitive for Canadian students than for students from Asia. I think there are overall fewer students from Canada applying to Stat PhD students in the U.S. than there are from China and India (a lot of top Canadian students stay in Canada to get their PhD from UBC, UofT, Waterloo). There are also much fewer visa issues as well (for instance, Canadian citizens don't need F-1 visas to study in the U.S.).
I know former students from McMaster, University of Mannitoba, and Acadia University who were admitted to PhD programs in Statistics at University of Washington, Yale, and Carnegie Mellon. So I imagine that someone with an excellent GPA From McMaster stands a good chance at very good Stat PhD programs in the U.S. (though the top 5 might be hard to break, as @cyberwulf mentioned). 

I think it is definitely less competitive for Canadian students than for students from Asia. I think there are overall fewer students from Canada applying to Stat PhD students in the U.S. than there are from China and India (a lot of top Canadian students stay in Canada to get their PhD from UBC, UofT, Waterloo). There are also much fewer visa issues as well (for instance, Canadian citizens don't need F-1 visas to study in the U.S.).
I know former students from McMaster, University of Mannitoba, and Acadia University who were admitted to PhD programs in Statistics at University of Washington, Yale, and Carnegie Mellon. So I imagine that someone with an excellent GPA From McMaster stands a good chance at very good Stat PhD programs in the U.S. (though the top 5 might be hard to break, as @cyberwulf mentioned). 

Although OP is an international student, she does attend one of the top four universities in Canada and has a high GPA. And I believe applicants from the top schools in Canada are treated similarly as domestic applicants in the admissions process at a lot of U.S. Statistics programs (Canada's a bit different than elsewhere).
OP: I think you have a good shot at a lot of very good statistics PhD programs (without the Masters), and so I concur with StatsG0d to apply directly to PhD programs. The top PhD programs are difficult for anyone to get into, so I would make sure to have a few "safer" options. But I wouldn't say that schools of the tier of University of Washington or Carnegie Mellon are out of the question for you.

If you're only considering the top stat/biostat programs, I wouldn't say there is much difference between them (stat vs. biostat) in terms of quality, training, or placements. For example, Harvard Biostatistics and Johns Hopkins Biostatistics have both placed exceptionally well not just for Biostat departments but also for Statistics departments. For example, these guys have PhDs from JHU Biostatistics and they publish a ton of work in top methodological and theoretical statistics journals:
https://sites.stat.washington.edu/people/fanghan/
https://yangning.stat.cornell.edu/
Of course, JHU and Harvard Biostat also have very good placements of their graduates as TT faculty in other Biostatistics departments too. 

Statistics departments tend to be a bit more theoretical than the majority of biostatistics departments. The top 5 biostatistics departments will have more theoretical coursework as well as more theoretical research (e.g. UW, Hopkins, Harvard, and UNC Biostats all have faculty who publish regularly in journals like Annals of Statistics and JASA-Theory & Methods and who serve on those journals' editorial boards). But for biostatistics, the further down the rankings you go, the more applied the department will be. Additionally, most statistics departments fund their students through teaching assistantships (though some statistics faculty who have a lot of external funding can support their students as research assistants), whereas biostat departments usually fund their students through RAs and external grants. This is in part because there typically aren't undergraduate biostatistics majors, whereas TA's are needed for undergrad statistics courses. 
It's not always so "cut-and-dried" though. You can do a mostly/entirely applied statistics dissertation in a Stat department, even ones that are known to be more theoretical (e.g. I know a few people from UPenn Wharton who wrote applied stat dissertations with little to no theory). And you might be able to do a more theoretical PhD at a biostat department, especially at a top one (one of my postdoc supervisors did his PhD work at Johns Hopkins Biostatistics on statistical theory for generalized estimation equations).  Your profile would be well-suited for either the top statistics or the top biostatistics programs. 
I suppose it depends also on your research interests. If you really enjoyed working on genomics, you could target programs that have strong faculty in statistical genetics (e.g. University of Michigan Biostatistics or UPenn Wharton Statistics -- at Penn, you could work with Nancy Zhang and Hongze Li). If you really enjoyed your theoretical math classes and wanted to keep doing similar stuff like that in statistics, you could focus primarily on Stat programs, with a few of the top Biostat programs thrown in there.

Your profile looks very strong. If you attended a top 3 university, I don't think it matters whether there is "grade inflation" or not. You have also taken a lot of graduate-level courses in both math and stat, and grades in grad school tend to be inflated anyway. Your research experience in evolutionary genetics is also a plus.
I think you should apply to mainly top 15 stats programs (according to the USNWR rankings). I'm sure you will get into several of them.

Your profile looks very strong. If you attended a top 3 university, I don't think it matters whether there is "grade inflation" or not. You have also taken a lot of graduate-level courses in both math and stat, and grades in grad school tend to be inflated anyway. Your research experience in evolutionary genetics is also a plus.
I think you should apply to mainly top 15 stats programs (according to the USNWR rankings). I'm sure you will get into several of them.

I imagine you will have no difficulty getting into any Masters program in Biostatistics, provided your GRE Q score is sufficient (aim for over 160, ideally over 162).  If you are contemplating getting a PhD later down the road, I would recommend taking a semester of Real Analysis in your Masters program (I don't see that you have taken this class, and at least one semester of it will be required for most good Biostat PhD programs). 

It should look something like this guy's webpage: http://www.travisfreidman.com/
Notice how he has his teaching philosophy, teaching goals, teaching competencies all very visible on his site. He also has a page for his teaching evaluations, including summary statistics, and he has the syllabi and course materials for the courses that he has taught. Your site should really sell your abilities as a teacher.
If you were to apply to a research university, you don't need to include as much (or anything, really) about teaching. A more "typical" webpage for someone seeking an R1 job would probably be something more along the lines of this: http://web.stanford.edu/~songmei/
 

6 total papers, I think... 5 of which were accepted/published (the other one under review) and one of which was in Annals of Statistics. 
As I said though, it isn't just about having some number of papers. It also depends on things like your research area and other factors beyond your control. If the search committee is, for instance, prioritizing applications from job candidates working in environmental/spatial statistics (say) and that isn't your research area, then you won't be hired no matter how long your CV is. If the department just recently hired somebody with very similar research as you, then they may opt to go with other job candidates who can "add something new" to the department. Search committees may also have their own preferences -- for instance, a member of the search committee might be really good friends with a job candidate's PhD or postdoc advisor, and they will forcefully advocate for that job candidate. It's stuff like that. 

It should look something like this guy's webpage: http://www.travisfreidman.com/
Notice how he has his teaching philosophy, teaching goals, teaching competencies all very visible on his site. He also has a page for his teaching evaluations, including summary statistics, and he has the syllabi and course materials for the courses that he has taught. Your site should really sell your abilities as a teacher.
If you were to apply to a research university, you don't need to include as much (or anything, really) about teaching. A more "typical" webpage for someone seeking an R1 job would probably be something more along the lines of this: http://web.stanford.edu/~songmei/
 

The elite LACs also care a lot about teaching, even if their research expectations might be somewhat higher than a "typical" PUI. So if you are aiming for an elite LAC, you should definitely try to obtain teaching experience. I recommend that those who are aiming for jobs at PUI's create a personal webpage that highlights teaching experience (e.g. you should put examples of your teaching evaluations or a "teaching portfolio" on there). Those aiming for jobs at research universities should emphasize the research aspect on their personal webpage.