... continuing our conversation from Reddit... lol
Yeah, your GRE score is kinda low, especially for Finance. I recommend you to really prepare for the GRE, then retake the exam. And/or try the GMAT (I did both, the GMAT worked better for me).
Your letters of recommendation should help you a lot.
I'm much less certain about your military background. It may be unique, it's probably a good thing. But by itself I don't think it means a lot for PhD applications.
About rankings and range of schools, they are always an issue here. Rankings for PhD can be dangerous. Rankings for PhD are very different from rankings for MBAs. A lot of factors are usually more important than ranking, like research fit. A lot of important factors are often ignored by rankings, like the quality of job placements. A lower ranked school can be much better than a top one, depending on your profile and goals. Your advisor can matter more than the school ranking. It's not so rare to find top researchers actually preferring lower ranked schools, since they can have more power, more influence, and more freedom. A school that is amazing for me may be awful for you.
So, there are many problems with the use of rankings to choose schools. I think the best solution is to develop your own ranking. That takes time and effort, but it should help you to increase your chances, and also to write better statements of purpose specifically tailored for the schools you chose.
But, in general, for PhD any top 20 school is usually considered insanely competitive, and a crapshoot. MBA programs can get lots of new students every year, PhD programs get only a few (for Finance, less than 5 new students a year per school, I guess). Even very strong applicants try a wide range of schools, typically you won't see people recommending to target only top 20 around here.