my 94 ford explorer with 140k miles is a salvage, beaten to hell, and is worth a grand or two. but not the right thing for you
i'd tell you to look for the same car i had as my first: a TOYOTA TERCEL; doesn't get much more "economy". fuel efficient, reliable, VERY stripped down. i bet you could swing one under 200k miles for a grand or grand and a half if you're careful
i don't know of a better choice. but really, at that price, your options are limited anyway, so i'd say: forget about looking for a SPECIFIC CAR, and just do a lot of prowling: autotrader.com, local papers and traders, and best of all: folks with signs in their car windows.
what you might want is like an old ford taurus or something, driven by a grandma
here's the real trick: whatever you do, MAKE SURE YOU TAKE THAT CAR TO A MECHANIC you trust. if they won't allow it, walk away. i've done this with the cars i've bought, and though it'll probably cost you $50 or more for a good check-out (make sure they pressure-test your engine ), it wil be worth it, either to know when to walk away, or to be able to talk the person down. have them list ever problem and use it as a bargaining point. BTW: if i were you i'd search for cars $2k and lower, you will have to do some negotiating to get a good deal
also: check for rust everywhere, get under the car, look all over, crawl under, don't be shy