COMonteCristo

Hi there!
I graduated in December 2018, took a 6 month long hiking trip, and here I am now applying to jobs and grad school. Ideally I'd like to work until grad school starts next fall. 
I am a rising senior who will be applying to PhD programs in statistics with interest in stochastic processes, time series, high-dimensional statistics, and uncertainty quantification. Not really interested in biostats even though I have a couple of experiences with biomath research.
Undergraduate Institution: UNC Chapel Hill
Majors: Statistics and Analytics
GPA: 3.81/4.0
Major GPA: 3.97/4.0
Type of Student: Domestic Asian Male
Courses taken:
Math:  Calc 3 (B+) (fml was lazy )  Linear Algebra (A) Economical Statistics(A) Probability (A-) Differential Equations (A) Discrete Math (A) (proof class basically) Statistical Methods I (A) Spreadsheet models (A) Intro to Optimization (A-) Stochastic Modeling (A) Simulation (A) Advanced methods of Data Analysis (A) Other:   Intro to CS (A) MicroEconomic theory (A) Corporate Finance (A)  
GRE General Test:  161 V/ 166 Q/ 4 Writing
(Should I retake this and try to get 168+ Q?)
 
Work experience (internships):
Statistical Consultant at Deloitte 2017
Actuary at Lincoln financial ( 2 exams completed) 2015
 
Letters of Recommendation: 3 strong letters from professors. 1 From humanities, 2 from stats
Masters:
UNC stats
UNC biostats
NC state Stats
Wake Forest stats
Would I be competitive at these places? Would these be considered safety or reach schools for me? Should I apply lower down the rankings list to secure a safety school?
As for why I didn't apply for any outside of state programs is I'd rather not be 120k in debt after since most masters places dont provide any assistance. I'm not sure if its worth it to apply for out of state masters like  Washington/ Uchicago? Am I wrong to think this way?
PHD:
This leads me to consider phd programs due to funding as well.  I want to do around 10 applications so that leaves 5-6 PhD programs I can apply to. Do you think I would have a decent shot at getting into my state PhD programs such as UNC or NCstate? What about the top programs like Stanford, Berkeley, Harvard, Washington, Duke, etc.?
 
Thank you so much for reading this and have a good day

Definitely agree with above, those schools you added and schools like Minnesota/Wisconsin should be the bulk of your applications, with a couple reaches like Duke.  Penn State also has a great statistics department, so talk to professors there. Those last three schools I would say are in the safety range (though nothing is guaranteed), so I don't think you need to apply to many schools at that level.

It could possibly help your application to ask one of your LOR writers to mention that you plan to take certain advanced math classes in the spring semester of your senior year (like Real Analysis II and whatever other advanced math/stat classes) to ensure that you are prepared for graduate school. But the most important things are the grades on the transcript you submit with your application (which won't have your spring 2020 grades) and the letters of recommendation.
I think you should do well in admissions for most of the schools ranged 16-40 and your chances are above average at Duke and UW (conditional on good performance on the GRE and in Real Analysis and Advanced LA). Penn State has a good reputation, and physics majors who have also taken some advanced math (namely real analysis) are usually looked favorably upon by Statistics adcoms. In fact, an alumnus who just graduated from my PhD alma mater got a TT job at University of Minnesota Statistics (without a postdoc) and his undergrad major was Physics.

Assuming that you score well on the Quantitative section of the GRE and get A's in Real Analysis I and Advanced Linear Algebra, I think you have a definite shot at NC State and possibly Duke. Conditional on strong performance there, I think you could even try applying to a school like University of Washington (though this is possibly a reach). Physics is a hard subject, and your GPA is pretty good. 
I'd recommend adding a few more schools like Wisconsin or Minnesota too.
 

What sort of state school do you go to? Berkeley vs Montana makes a difference. Also, it's hard to say without your GRE score and those future math grades if they'll be submitted. Do you expect to get a 165+ GRE Q and do you think you'll get an A in analysis?
So much depends on these 3 questions that I'll refrain from giving too specific advice right now, but I'd say those top 3 schools are going to be your reaches (but perhaps obtainable) and the bottom 3 are probably low matches - there's a big gap where you skipped like 30 spots in rankings that are probably your best fit.