Don't be afraid to ask the seller plenty of questions. How long has he or she had the car? Has it been in an accident? Does it need any repairs? Why is it for sale? Does the owner have the title? Is the car currently registered? Coupled with an inspection and history check, the seller's answers will give you a better idea about the car's upkeep.
Just because you are getting a car on the cheap doesn't mean you can't negotiate. In this price range, assume that the seller has priced the vehicle a couple of hundred dollars above what he really wants for it. With that in mind, it doesn't hurt to look at cars that are $1,500 or so above your price range. You might be able to bring the price down if the seller is willing to negotiate. And if the car needs repairs, you can use this fact to negotiate a lower price.
Use the Edmunds used car appraiser to determine the current market value of the car. Then, use the appraiser as a way to depersonalize the negotiation. On the phone, ask the owner how he set the price. And you can probe a seller's willingness to negotiate on the phone by asking if he's flexible on price. Make an offer slightly less than what you want to pay to give yourself some wiggle room for a counteroffer. But don't commit to anything without having first looked at the car.