Civic not bad, keep your mind open, do CL searches in the ~$1k range, and just go example by example. There is not a predictable market for $1k vehicles, they vary widely.
That said :
Ranger/S10 4-cylinders
Civic/Corolla/Tercel
Volvo 240
'90s Cop cars (Caprice/Crown Vic)
Box Vans (lots of cheap/reliable ones out there, if you don't mind looking like a child abductor / speaker salesman)
If your goal is cheap reliable transportation, you might have to take something that isn't all that fuel efficient, depending on what's available.
It can also be advantageous to get something that's got some body damage, as generally that lowers prices dramatically. Again, it's just an issue of looking at the vehicle for pure practicality purposes. I know a guy who bought an '01 Maxima SE for $1,200, it had 70k miles on it and ran perfectly, but had been hit high on the RR quarter panel, smashing it in a couple inches and popping the trunk out of whack enough that it wouldn't close properly (rain gets in it, etc). Makes a really good cheap nice DD for him, and he doesn't worry about the cosmetic problem or the lack of a usable trunk, he'll worry about that when his work picks up and he can afford a car.