First of all, you can ask questions about the horse itself:
Behavior, how's travelling, if he used to going out to the paddock, what are his defaults, how's reacting to new things (competitions,...) if he had been sick someday etc. After, questions about the work: what he knows, what he likes to do, if he already did competitions, the rider's level he should have, if he can work with or without other horses.
Of course, as Kareen said, you have to meet a good seller (not an easy thing) and choose your vet really well, some of them do wrong visits!!!
You should ask as many questions as possible (hopefully the breeder would be honest, which isn't automatic). If possible go with a professional, and of course, the control vet! With a vet that we know, and not a vet that the breeders know! The best is doing a blood test, to see if the horse had had an injection before the visit which can make the results wrong!