My first horse was a terrible match for me, but because we had no idea what we were doing, we bought her anyway and it was a disaster. She was too young, too hot and it destroyed my confidence as a rider. I finally sold her and moved to another barn where I could learn to jump. I started out on the best school pony ever and regained my confidence and improved my skills, all while keeping an eye out for a horse of my own. But each horse we went to look at, my husband would video tape the ride (if we even got to that point) and I would take it back to my trainer for an eval. Sometimes you could just have the seller send pics and a video so you wouldn't have to waste your time riding a horse that was lame in the first place.
Anyway, I ended up finding a wonderful 10 year old horse that had all of the experience I needed, had been shown, wasn't spooky, etc. My confidence is back and I love riding again. We have been showing and doing well and I think we will only get better as a team.
I totally agree with having your trainer help you find something when you are ready. Trainers also have a lot more resources than you might and they might know of several horses for sale, that aren't actually advertised. Just take your time and in the mean time enjoy learning on the school master. They are the best and worth their weight in gold. Good luck!