Foreign Service won't care which type of degree you do. If you don't like theory, don't do a theory-based degree. The Foreign Service won't care whether you went to an APSIA school. If you want to do government service at all, getting a master's is necessary at some point for career advancement but it doesn't matter where it's from, but the thing you need to consider is that your career trajectory/priorities might change. By that logic, a professional degree will serve you better. And by that logic (again), just choose the best umbrella brand name you can (i.e. the best university that has a public policy program you can get into). No one will know or care what you studied 5 years down the line; at most, they'll think "Oh, this person went to University of X--I went there as an undergrad!" not "Oh, he did a theory-based IR program instead of a blah bla blah." That doesn't happen.