Check with local mechanics which cars they drive and dealers the buy from. Tell them your budget and needs and you'll find they're pretty consistent in their recommendations.
Also, don't overlook dealers in favour of buying direct from owners, both have pros and cons.
Dealers have to allow you to return the vehicle within a certain time frame, their name is also on the line. Some offer warranties to fix anything that goes wrong in the first x years. Do your research, but for old cars this can be a valuable saving. Also, some dealers offer to provide you with parts at cost for the life of the vehicle, also potential savings.
Don't go in on a Saturday, do go in near the end of the month. Go back several times, compare, negotiate.