Experience in cross country, stadium, and dressage. Make sure they can jump with no problems, and can do most dressage things you want to do. Good temperament! (And if you are getting a mare, see if they are still good in heat or if they become a monster!) And of course you want to really have a connection with them! Good luck!
Make sure the confirmation of the horse is correct so the horse is able to perform effectively and won't get injured very easily
Cross country experience, something that isn't fussed about anything, that'll jump anything you point it towards without hesitation and if you're wanting to compete make sure they have decent flat work to pull a good dressage test