Cars in the $10K price range and below as far as condition is concerned is more about how well the previous owners cared from them, and less about the brand and model. In general Japanese cars hold up well over time, exception perhaps is Mitsubitshi. Other Asian cars have improved (Kia, Hundai) but some models are better than others. Old Subaru’s don’t get very good mpg, and the AWD systems are expensive to repair if previous owners ran mismatched tires on them. Honda Civic is more to buy due to high resale values but do hold up well.
European cars (Volvo, BMW, MB, VW, Audi) are all very expensive to maintain and repair when they get old and have higher miles on them. If you buy one of these a multi thousand dollar repair bill is very common. Volvo’s are the worst, with $1,500+ repair bills more the norm than rare. A new or rebuilt auto transmission is commonly needed with aging VW’s and Audi’s and you are talking $4,000 for one.
Basic domestic brand small cars are your best value in terms of low cost to buy, with reasonable repairs and maintenance. Exception is Chrysler small cars, Neon, Stratus, etc. They just aren’t well made cars and need frequent repairs. Ford Focus is good. Chevy HHR, and Cobalt are OK.
Frequent and expensive problems with $10K and under cars is the auto transmission fails. A manual transmission is my preference over an auto trans for longevity. Too many previous owners did not have regular transmission fluid changes making the auto transmissions prone to fail at or before the car reaches 150K miles.
A mechanic can inspect a car and tell you if it has a bad head gasket, and other significant problems at that moment in time. A few miles down the road things can and will break down, but the inspection with pressure tests of the cooling system, and compression in each cylinder will go a long way in avoiding expensive motor problems.
You need to use gates.com web site to learn if a motor has a timing belt or timing chain. A used car with a timing belt is often due for a timing belt job (90K to 105K miles or every 7 years is common replacement intervals) which means a water pump and other parts too. Gates will tell you if it is an interference motor or non-interference motor. Interference means the pistons hit the valves when a timing belt breaks. The resulting damage means a new engine in most cases, $3000 and up. Used cars are for sale for a reason. That reason could be a big repair bill which the owner decided to avoid and get another car.