Getting a car loan with bad credit?

Question

When I was 18 I got a couple credit cards and payed them good for a year, then my job went shaky and i was out and no way to pay them back. Im now 21 with a credit score of around 510. Since then I have gotten a very good job, and wanting to get a new car. Im thinking of getting a car thats around 15-17k dollars. Would it be possible with my credit? How big of a down payment do you think I would need. I have a decent car I can trade in now, or sell maybe for around 2k. And can probably come up with around 1k to go with that for a downpayment. Would that be a pretty good downpayment on a loan amount that much? I also plan to pay off those credit cards which wasnt that much, most of it now is just finance charges. Will that help my score a lot or will it still be pretty low if those negative things are on there even if I payed them off...