+1 to what jtsanders stated.
A make and model that is supposedly a reliable choice will absolutely NOT be reliable if it has not been maintained properly.
When buying a "cheap" car, the maintenance that it has received from its previous owners (there could have been many) is the most important factor. So--although this is not necessarily a realistic piece of advice regarding an older, inexpensive car, you should really focus on those that come with full maintenance records. That will almost surely eliminate cars from car lots, and should drive you to look at private sales.
As jt stated, a car that was owned by an older person is more likely to have been maintained properly, and is more likely to have maintenance records available. And, the added bonus is that a great many of those older folks have chosen to drive Buicks, Ford Crown Victorias, or Mercury Grand Marquis vehicles--all of which are among the most reliable cars on the road today.
Your "not" son should forget about "cool" cars and should focus on those that have a proven record of excellent reliability and requiring less maintenance than higher-performance models. Those Buicks, Crown Vics and Grand Marquis may not look cool to him, but they are much more likely to spare his wallet than vehicles that are more "hip".
If you can locate a well-maintained model of one of the above-referenced makes, you will probably be finding the best "cheap" used car for him.