Vet Check with a vet you trust - NOT THE OWNER"S VET! If you don't have a vet get a recommendation from someone you know and trust.
Don't get something outside your abilities. It's one thing for a first time owner to get a sound horse that isn't made and work on improving it (that's half the fun), it is another to get one that has no or poor training, terrible ground manners and other nasty habits when you aren't equipped to fix it...Unless you really know what you are doing, you won't be happy - just frustrated.
Have your trainer help you...it is worth the finders fee. They know where you are and what you need to succeed. If you find it on your own, get your trainer to ride it and try to take at least one lesson on it. If it is possible, try to get a try out for a couple weeks at your barn. If the deal is good, the owner should be willing to work with you to make sure you will be happy with the horse. After all, they should want their horse to be healthy and well cared for. If they don't seem to care what happens to the horse, be VERY wary.
Know what you have to spend, but don't buy a horse just because it hits that mark. You can find great deals on horses if you are savvy and smart, but for every great deal, there are probably dozens of bad ones.
If it sounds to good to be true.....