I saw at least a couple dozen horses over the course of a few months before I finally found "the one." I think I was in a similar mindset as you at the time- my confidence had been damaged by the horse I had been leasing (long story ) and I just wanted a sane, sensible horse to do local shows, trail riding, and maybe some jumping. I knew that my horse was the right one the first time I rode him when I asked him back down to the trot from the canter and he didn't get rushy or hot, he just did what I asked him to do. And that's been my experience with him ever since- he's incredibly eager to please.
- Ask the seller to not have the horse already out and prepared for you- ask to go out and catch the horse yourself (if he's in a pasture), groom him, pick up his feet, saddle him up, etc. yourself. And don't even let the owner stand at the horse's head. I almost bought a horse that was OK when the owner was there holding her, but was too dangerous to complete a vet check without her!
- Trial period. Don't buy a horse without one. I'm glad the aforementioned horse had a trial period or I'd have been stuck with a horse that needed to be restarted from the ground up! If the seller won't do a trial period and you really like the horse, at least do multiple visits and ask to ride in & out of the arena, on trails, etc.
- Get a vet check. Keep in mind that the horse doesn't have to be in "mint" condition, but does need to be sound for the types of activities you have in mind.
- If you have second thoughts about the horse, it's probably not the right one.