Bought a few cars myself, all private party. Some things you definitely need to do:
1. Inspect the car yourself (lights, leaks, interior, etc.) and do a driving test. Check the tires levels before you go, as most folks have under-inflated tires. Some cars start high in RPMs and then settle down at the 1k level, so make sure to let it sit for a minute before putting it in gear. While driving it, find a nice straight stretch of road, center the car and the wheel, and let go of the wheel for as long as you feel comfortable - at least 5 seconds, hopefully more. You can see how well aligned the car is. If it drifts left or right, that's usually the sign of an accident.
2. Ask to see the service records on the car. Hopefully your seller kept track of oil changes and repairs, timing belt changes, etc.
3. If you're still interested in the car, get the CarFax.
4. Negotiate a price, SUBJECT to a mechanic inspection. Meet the seller at a 3rd party mechanic (not a friend of his or yours, though obviously skew towards yours!) and tell him/her the situation - you're thinking about buying this car and want to have it checked for leaks, previous damage (bumpers, chassis, etc.), brake pad levels, tire wear, shocks, struts, filters, emissions levels, etc.
*Be aware* - while this will cost you some money, probably around $100 (call a few local mechanics first to get a rate), it puts you in a powerful position to negotiate a lower price, based on repair costs and such - which you can elect to do post-sale or not. Because you've already agreed on Price A "subject to the inspection," you can say "well, it's got x, y and z wrong with it - how about Price B instead?"
As has been mentioned, stick with manufacturers for which you can get relatively cheap repairs - that is, companies still doing business in the United States. Try and stay away from niche manufacturers, as the money you save up front will kick you in the ass later.
Good luck on your endeavor!