HK2004

I'm a little late to this. 
 
I had a really low GPA (about the same as yours) and got into a solid enough program even without doing a Masters afterward. So with the combination of an undergraduate thesis and good performance in an MA program, I'm willing to bet that you won't face too much of a problem with your grades alone. 
 
Graduate admissions chairs don't help with squat. The only thing they might be able to do is give you insight about "minimums": I know some schools post that they "require" a 3.0 undergrad average, so an admissions chair may be able to give you perspective on how stringent that is, and what that means for your application. But everyone says they do "holistic" readings of applications. Based on my experience applying, I actually have to say I do believe it. 
 
So about contacting POI's.
 
Some profs are open to it, but it's really only best to do that if it is absolutely clear that this is a person you'll want to keep in touch with. That is, don't just email some prof who you think is gonna be on the AdCom and remember your name. So you're presumably IR/Conflict, right? If you're interested in a certain topic (e.g. civil wars), maybe email a prof whose work has really influenced yours and introduce yourself/tell them you're applying to their school/thank them for being a positive influence/briefly make a general mention of your interests, and that you hope to be in touch over the years.
 
That's really all you can do, and chances are you'll at least get a sentence or two in response if you're a decent enough human being in your message. Worst case scenario, you've just networked with a good scholar, and if you keep in touch with them, it can help your professional acumen. 
 
At the end of the day, when it comes to contacting profs, it really just is about being genuine. Believe me, they can tell the difference between someone who's genuinely interested in their work who happens to also be applying to their school, and the person who wants to get into their school and read their CV to butter them up as a potential "in." There's no magic formula, really: in this field, everyone's really interested in their research, so naturally it only makes sense that the more relevant they are to your research (as opposed to their relevance to your dream school), the more likely it is that they'll respond positively to you reaching out. I've cold-emailed really big names at really big schools and have gotten nothing but warm replies from all of them, so just in my anecdotal experience I've never had any reason to feel like profs aren't open to being contacted so long as you're genuinely interested in what they do.

I am hoping to apply for a PhD in Public Policy (potentially Social Policy), but I keep seeing how important rankings are to everyone and I'm not sure which list to use. Some schools change rather dramatically from list to list. They are also usually listed as Political Science, which isn't necessarily the same department. I'm looking at schools outside the US, which confuses the lists even more! Does anyone know what the definitive "list" is for Public Policy? I was considering the University of Leeds and McMaster (Canada) due to research interests, but neither program is very highly ranked. How much does that matter? Sorry for all the questions, I'm new to this.

Applying to 25 programs would cost you a fortune. But if money is not an issue, I suppose it won't hurt.
 
Remember only to apply to schools that you wouldn't mind attending.

I agree with HK2004. There are a number of good policy-oriented PhD programs in the U.S. that might be worth looking at (Georgetown's PhD in poli-sci is not one of them though). JHU-SAIS, Tufts-Fletcher School, Harvard-Kennedy School, Princeton-Woodrow Wilson, U Pittsburgh-GSPIA are all places that has policy oriented PhD programs. There are also other schools that are more leaning toward Public Policy like RAND-Pardee but I don't know if that kind of a route is how you'd like to proceed. It might also be a good idea to check out the Professional Programs - Government Affairs forums, since such programs kind of fall into their jurisdiction.

Superfly, I'd definitely recommend talking to someone outside of an internet forum about this. What I'm hearing is that you're looking to get into a policy-type PhD program focused on development and diplomacy, and you'd like to tailor your studies in such a way as to both build upon and subsequently further your current career trajectory. 
 
The PhD in the U.S., from what I've gathered, can be a huge minefield if you're not careful. The best school for me may be a horrifically bad school for you. Off the top of my head, I'd point you towards looking into any school that's attached to a lot of professional institutions: major schools in metro areas like Georgetown and Tufts might be a good starting point. Other possibilities include a policy-focused degree program like Columbia's SIPA or JHU's SAIS, or even UCSD's IR/PS if you're into Pacific Studies. Like Lemeard said, your scores may prevent you from getting into a top program, but this isn't an area that I have any experience in (i.e. policy/practice-oriented PhD applications) so I just can't tell you for sure whether your professional background will help mitigate it.
 
You just have to be really careful. That's my best advice. Talk to an academic, get in touch with a school's graduate coordinator...anything you can do to sift through the incredible diversity of programs out there. You don't want to get into a situation where you get into some big-name school only to find that they either don't do the research you want to do, or that they take a radically different approach than you wish to take. Especially since you seem to be coming in with enough background to really know what you're focusing on, I feel like that makes it all the more important to do your homework. Sorry I can't be of more help.

Orlien, I was literally in the exact situation you're in. My advice is different from the other three posters here though, so obviously I'm not offering gospel. But it's noteworthy that my stats (both in PoliSci and overall) were far worse than yours: I graduated with a sub-3.0 GPA, got into a Top-30 program, and was offered a university fellowship at a 50-ish program. So it's not impossible, or maybe I was just lucky. 

What I can tell you is that it helped me to include it in my SOP, based on what I gathered from students/faculty at the school I accepted admission from. But I limited my mention of this to a single, tightly worded paragraph. I focused primarily on what I gained from Natural Science courses (e.g. scientific inquiry, research design, intellectual stimulation, work ethic, etc.), and framed it as "while I found myself drawn to the art of scientific inquiry, I learned the hard way that the natural sciences were not an area in which I could excel" (all of which is true!)... I also specifically referenced the grade discrepancy, and made mention of my motivation for taking natural science courses (to address concerns about my commitment to PoliSci). 
 
Again though, this was a single, small part of my SOP. I placed it within my SOP such that it wouldn't interfere with the main thrust of this document: in other words, I didn't harp on it, didn't try to explain it, just pointed it out and gave my brief thoughts on it, and moved on to focus on the rest of my experience/purpose. Basically, be honest, forthright, and concise about what you clearly (and rightfully) feel is an important anomaly to point out.

I did also talk to my LOR writers about including it; I haven't read the recommendations so I don't know what they did, but you can never go wrong with that. Feel free to PM me if you wanted some more specifics.

Orlien, I was literally in the exact situation you're in. My advice is different from the other three posters here though, so obviously I'm not offering gospel. But it's noteworthy that my stats (both in PoliSci and overall) were far worse than yours: I graduated with a sub-3.0 GPA, got into a Top-30 program, and was offered a university fellowship at a 50-ish program. So it's not impossible, or maybe I was just lucky. 

What I can tell you is that it helped me to include it in my SOP, based on what I gathered from students/faculty at the school I accepted admission from. But I limited my mention of this to a single, tightly worded paragraph. I focused primarily on what I gained from Natural Science courses (e.g. scientific inquiry, research design, intellectual stimulation, work ethic, etc.), and framed it as "while I found myself drawn to the art of scientific inquiry, I learned the hard way that the natural sciences were not an area in which I could excel" (all of which is true!)... I also specifically referenced the grade discrepancy, and made mention of my motivation for taking natural science courses (to address concerns about my commitment to PoliSci). 
 
Again though, this was a single, small part of my SOP. I placed it within my SOP such that it wouldn't interfere with the main thrust of this document: in other words, I didn't harp on it, didn't try to explain it, just pointed it out and gave my brief thoughts on it, and moved on to focus on the rest of my experience/purpose. Basically, be honest, forthright, and concise about what you clearly (and rightfully) feel is an important anomaly to point out.

I did also talk to my LOR writers about including it; I haven't read the recommendations so I don't know what they did, but you can never go wrong with that. Feel free to PM me if you wanted some more specifics.