so, i just bought a car with roughly the same budget, and my advice is to buy a 2000 to 3000 dollar car instead because you will need the extra money to insure it and to help pay for the first mechanics visit. As an example i paid 2500 for my car(92 miata), 2000 on taxes and insurance,and then dropped the car off at the mechanics and told him to check and replace anything that might be a problem which costed 1500 + 1000 for new suspension because mine was worn and had a cracked rear spring
basically my 2500 car ended up costing me around 7000, of course I could of done it cheaper by not buying year long insurance and only replacing the necessary stuff(or buying a car with a more complete mechanic record, mine had none) but it still would of costed much more than the original price so keep that in mind