Not certain if you qualify for graduate programs or not; I have no experience with those and it'll vary by manufacturer.

3K downpayment, on roughly how expensive of a car?  Assuming the cost of the vehicle isn't way out of whack in comparison to the DP or your income (DTI looks fine offhand), you'll certainly get financing of some sort.

Interest rates may be all over the map if you only have the one tradeline with the lates from 2008; check into your local credit unions and probably with your bank before going down to the dealerships.  You can find some lenders online too (check in the auto approvals thread) or apparently lendingtree has now extended their network of auto lenders as some people have reported good success there recently.

Refinancing isn't a big deal, you just get a 10 day payoff quote from your current lender, and start shopping it... exactly the same process as getting a car loan initially except for the quote requirement, and of course no dealer financing.

---

Starting Score: EQ 561, TU 567, EX 599* (12/30/11, EX lender pull 12/29/11)
Current Score: EQ 660, Wally TU 697, EX unknown (05/13/13)
Goal Score: 680 in all three (01/01/14)

Take the FICO Fitness Challenge