My own personal experiences with USAA have been very positive.
I have checking, savings, and insurance with them, and until just recently, owed them a gazillion dollars from my USAA CC that I crashed and burned.
I was speaking to one of their reps last week, and like I told her, they're so nice it's actually almost fun to call them. I think it would be a great place to work because you'd constantly be having your adoring public falling all over you to tell you how great you are. Sort of like being a rock star or pro athlete, only more like a 9 to 5 job and a lot less money.
Anyway, the rep was nice enough to tell me that for a USAA CC a score between 630-644 qualifies for prime + 15.65%, and with a score of 645-659 one would qualify for prime + 13.65%. YMMV. We theorized that I didn't qualify because when I applied my score was probably below the treshold, and she agreed that a reasonable strategy would be to try again next month.
While I was talking to her, I asked her about a USAA secured credit card. She transferred me to someone else, who said she’d mail an application. The secured CC is backed by a two-year CD. You can open it from between $250 to $1500.
So, to answer your question, you will probably qualify. However, you might consider just calling and asking. They'll probably be willing to offer some pretty useful guidelines.
Starting Score: TU 737 EQ 721