I could afford up to $1000/mon car payments
That's insane and I would not recommend.
As I see it, you have two options:
- Buy a $3k car (and realize that a $3k car may be missing some modern safety features like stability control and may need some work, although should not need *major* work unless it's a newer and/or unreliable car)
- Put $3k down and finance a slightly more expensive car. I have no idea what your income is, but I would definitely aim for less than $8k, probably $6k-$7k as that will get you a new-ish car in decent shape.
The 2nd option carries a few more risks and more money spent, as 1) you may have to pay interest if your credit history is not long, 2) you have to take out full coverage insurance for a financed car, and 3) you'll have a monthly payment ($4k over 36 months is ~$111).
Also, if you have never had car insurance, your insurance is likely to be on the higher side.
Anyway, some model options. Depending on the mileage and year, several of these can be around $3k, and a little more for the newer years/less mileage.
2006-2010 Hyundai Elantra
2005+ Hyundai Accent
200x Toyota Corolla or Honda Civic
200x Honda Accord or Toyota Camry
2005-2013 Toyota Yaris sedan
2003-2009 Mazda3 sedan
I don't know what region of the country you are in, rust may be a major problem for some older cars. (Not an issue in California...) Always get a mechanic to check out any used car before you purchase it.