If you buy a $1,000 car, you always have to be careful of when where and how you drive--make peace with fact that it can die at any time (and take the precautions necessary), but I am sure you are aware of that...
Having said that, let me assure you that A GOOD USED CAR CAN BE HAD FOR $1,000. I have been driving cheap cars my whole life (and have been served well by nearly all); I am not a mechanic--there is plenty a person with no mechanical inclination can do to protect themselves.
Here's a list:
Only buy from an original owner (don't buy from a dealer under any circumstance, used dealers at that price will screw you, plus there is no chance of getting a deal from a dealer, he knows what it's worth).
Only buy from a rich neighborhood (rich people take care of their cars better than poor people because they can afford it, and on occasion the rich undervalue their car or they consider their time too valuable to mess with selling a car).
Read local small newspapers in well-to-do areas near you and check their classified ads. Check bulletin boards at grocery stores. Cruise good neighborhoods and look for "FOR SALE" signs (but zoning laws mean less people do it this way, and watch out for cops who will pull you over for no reason)
Make sure the person you buy from has maintained the car well, and ask to see the records.
Use common sense, if a person makes you uncomfortable or seems nervous or shifty, or seems like an irresponsible person, pass. If the seem in a hurry to get rid of it, be weary 9but don't necessarily pass).
Wake up in the morning, get to the car before the dealers and other people who need a car (it's very competitive)
There are exceptions, but don't buy from a young person unless it's obvious they took it easy on the car and had mom and dad backing them for maintenance.
BUY A HONDA ACCORD. Or at least buy something simple. If you can drive a manual and you know what a good clutch feels like, buy a manual (they have less tranny problems).
DO NOT BY AN AMERICAN MADE CAR PREVIOUS TO 1990; If you find a cherry domestic model, than don't pass it up, but all things being equal the poor commuter must drive a Japanese car, something small.
Don't buy a sporty car (go for it if you really need fun, but the sportier the car, the more likely you will need AAA). DON'T BUY AN OLD IROC FROM A GUY WITH A MULLET THAT PULLED STUMPS WITH IT.
Don't buy anything with more than 150,000 miles on it (but again, there are exceptions if it's really cherry).
Think about how sharp your seller looks, how ruthless they look. Rich people, all people, will screw you.
Check out the cars parking space--any fluid?
Check the oil--is it really dirty, does it need some oil?
If it's an auto, check the tranny fluid (any flakes/particles in there).
Check the exhaust while it's cold, any oil in there?
Be safe, but drive it at high speed if you can. When no one is next to you, take your hands off the wheel a little, is it pulling to one side or the other?
Try to hit the brakes hard--does it pull to one side?
Check the tread on the tires--put a quarter in there (does it go half way in?).
Be weary of a recently cleaned engine.
DON'T BUY A CAR WITH ELECTRICAL PROBLEMS.
DON'T BUY A CAR THAT'S BEEN IN A MAJOR ACCIDENT.
Make sure the frame is straight
Make sure the brakes aren't mushy.
Don't go looking in the rain (you need to hear things that the rain can drown out).
If you know a mechanic you can trust, take him with you, but realize that most mechanics will either overstate what's wrong (so they can get you or the owner to "fix it"--or if the car is a really good deal they will get you down on the car so they can get a shill to buy it later).
Try to take your folks with you (even that nice old lady will try to take advantage of a young person by himself).
Make sure all the documentation is in order, and that the title doesn't say SALVAGE.
Carfax reports are over-rated; I personally wouldn't waste my money. If you follow the above rules, you'll be fine.
If you buy a car used it's pretty much AS IS in every state, but if it breaks down right after you bought it, go back to the person you bought it from and let them know you can't afford what happened (a decent human being will kick a few bucks back your way).
Bring cash with you, negotiate--sometimes a car out of your price range can be had if you wave a little green under a person's nose.
In summary: buy a Honda Accord (nothing else like 'em) from a rich person with a family living a mid-life suburban nightmare; make sure they have plenty of maintenance receipts and check the driveway; if the car feels solid make them a cash offer and let them know you're ready to drive it away so their weekend won't get spoiled.