Is it feasible for you to spend $2-3000 cash? I think the answer is yes, since you're considering spending 10k on same.
You can get a reasonably new (10 years) car with decent gas mileage and a lot of life left for that price. Generally speaking, reliability is better in Japanese cars, but I've read the Ford Focus is pretty good, and it might be cheaper than a Corolla or a Civic. We've never had a new car (our Subaru is from 2003 and we bought it last year - super excited to get into the 2000s), and it's never been a problem. Buy cash, have your oil changed regularly and other basic maintenance (brakes, fluids, spark plugs), and you'll be out a lot less than if you bought something for that kind of cash. If you're concerned about reliability, then set aside some of that huge 10k fund you are going to drop on your student loans just in case.
Good luck!