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.
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