You can easily find a late 80's GM a-body (Chevy Celebrity, Buick Century, Pontiac 6000, Olds Ciera) in good shape for $1000. They came with the 2.5L "Iron Duke" I4 or the 2.8L 60* V6, you can't go wrong with either of them as they are both very reliable and easy to work on. Not to mention there are dozens in salvage yards if you need parts.
I'd also recommend an S10 or Ranger although they aren't exactly the safest vehicles on the road. 1st gen Cavalier or Sunbird would be a good option, as well as an early 90's Lumina or Grand Prix.