Well maybe bring someone that knows about CARS, just to check for common problems, like KezR33 said, engine noise, rust and all that.
Definitely need to take it for a test drive, to see if there's any unusual noise, verbrating or steering problems etc. When you do take it for a test drive, don't drive it like a granny lol, do some quick accerations or some emergancy braking or some other manuvers to test out the cars abilities.
Also, there's no harm in going back there the 2nd time, but bringing someone else to check over it.
And I guess once you are happy with what you see and how it drives, then pay someone the money to get it check fully.