Employment history is whatever: show your last two paystubs and that covers that... this isn't a mortgage. Your downpayment is excellent even without the trade-in, 1/3 on a new car, complete win.
The only issue you might have is income: you gross 1600, and you're looking at roughly a 16k note over a 5 year period and possibly around a 10% APR on a new car... which is a note of roughly $350 / month. I know you don't pay a lot in taxes, but this is a pretty big expense for your current income, and I concur with the prior poster: see about getting a cheaper used car instead. Even at 5% financing if the captive dealer lender is in a good mood, is still $300 a month, again likely too expensive. You're getting a loan of roughly the same amount as your approximate annual after-tax compensation Too much in an uncertain world.
You might well be able to get a Sonata just off lease, you may pay a little more finance wise, but you probably knock a good 5-8K off the price at the dealer, and you may still get a good finance deal from Hyundai directly, they appear to be pretty willing to deal with subprime / rebuilding credit folks. Just a swag, and this is conservative, a 2009/10 off lease, knock off 1/3 for depreciation, now you're looking at like ~$170 / month at 10%, and if you get an ugly loan like mine (19%) which is a lot more you're still only at $210, and both those numbers are a lot more defensible on your income.
One trick you might want to try, since you're rebuilding, get a 6 year loan instead of the 5, and be planning to refinance in six months to a year as your credit scores keep improving. This might save you a little on the APR, and also on a lower payment, you have more opportunity to throw extra money to pay down the principal faster, which is HUGE on a higher interest rate loan. Or any loan for that matter.
