So as long as DTI is in check and income is there, I think you have a shot at it. Definitely try with a CU or a bank your already have a relationship with. But I would take steps to address that collection first. Check out the links below and post in Rebuilding Your Credit if you need any help for that. I'd send a DV followed by a PFD if I agreed -or- I would call the OC and ask to pay it in exchange for them pulling it back. Paying the collection [agency] itself won't improve your FICO.
Credit Scoring 101 - great for knowing what is in your credit score and to see how your score is impacted.
What Steps Do I Take - great for learning the repair process.
and Example letters - PFDs, GWs, DVs, etc.
12k a year?
I'm not a credit guru like some other here, but I do know a lot of lenders require a certain amount of annual income to loan money. That is extremely low.
You can negotiate APR. That being said, with your annual income and credit score, you're a risk so the APR will be likely cost you.
Offer a PFD for the medical collection now. Have you asked the CA if it is normal procedure for them to delete after payment? Hopefully yes. If not, just pay it now and send GW letters. Make sure CA sends you proof of payment so if the CA is not marked paid or deleted before you talk to lenders, you can show them that the CA is already paid.
Your income is very low and has the chance of fluctuating while you are in school. I suspect that lenders might have a hard time justifying an approval with your low income. Most of the time auto loan payments should be about 7 to 11% of your gross monthly income. Some people advocate following the 20 - 4 -10 rule. In practice this is 20% down, 4 year loan, 10 % of gross income.
10% of your gross income now is ~$100 a month. With a 48 month loan and 20% ($5k) down, you can afford about a $9k vehicle. This is assuming that you can get an 8-10% APR. Edit: I realize most of your school and living costs are already covered right now. I would still caution against taking on several hundred dollar a month auto loan on your income.
First, I would try hard to get the medical CA to accept a PFD. Second, pay down your CC utilization to only a couple of hundred bucks on the highest limit card. That 16% utilization is killing you. Not to mention unless you are in an intro 0% APR period on all three cards, your $1k+ balance is more to worry about than the APR on a auto loan you don't have yet.
Your best bet to get the auto APR you want will be to begin a relationship with a local credit union. Once you get approved with a loan, then see if the dealer can beat it.