My advice is, in both cases (dealer or private) if you dont know what you should look for in a car for sale, take someone with you who does... You cant trust anyone, even an old grandpa, Private: if you buy a lemon you have to wear it unless you want to go to court, Dealers: most used car dealers offer warranty, but most warranty's arent worth the paper they are written on as they have large loop holes in them...
Just take your time and make sure you get what YOU want... I used to work for a car dealer and you would be surprised how far they will go to make a sale, you just have to push them.