When shopping for a used car, what criteria are most important? I am wondering how much weight I should put on the mileage, number of previous owners, carfax reports, and/or maintenance records. From my experience carfax reports don't really tell you all that much. I know the lower the miles the better, but just because a car has low miles doesn't mean it is a good buy. In addition taking each car I look at to the mechanic could get expensive. Also if I do take them to a mechanic what exactly do I have him check? Compression, smog check, and what else? In addition I'm in a new area and don't know any mechanics so how can I find a good mechanic to assist with this process? I'm in the LA area if that helps.

You call the auto club and ask for referrals. Then WHATEVER you are interested in buying gets checked out by THAT mechanic.

I do investigations and Carfax only lists what is reported to Carfax - and that is not everything!

Low miles do not mean a "better" car. A car that's been sitting has sludge for oil (among other problems).

You tell "your" mechanic you are interested in buying and ask for an overall opinion. It will cost up front but save in the long term.