The answer depends a lot on what you want to do with the horse! Is it to compete, to breed, or to buddy up with on hacks?
I'd stress that you must be 100% convinced and drawn to the horse subjectively, but should also seek external, objective advice, e.g. from your trainer (who ideally should not be in on the deal, to give impartial advice)
The most common mistake I see is inexperienced rider buying inexperienced horses in the flawed idea they may grow together. Inexperienced horse, experienced rider, and vice versa.
Good mind, scope, health and for sure our relationship at first sight🙏🏻
their temperament and potential
Make sure they r the right age/height and make sure they are loyal and do not bite and make sure they like you and r interested in you
You look for good conformation and you want to focus on the hind end rather than the front end. If they tuck their back end then that's good because you can train the front end but not the back end
Make sure you like the horse and that the horse likes you. I know it sounds weird but horses act differently with different people and a horse that isn't too fond of you will be harder to cooperate with
Decent confirmation, how they move &a carry themselves, temperament and personally I look at breeding too
Temperament, how you get along with the horse, how they act on the ground vs how they are when you ride them, breed, age, price.