I would stay away from gaited and go with a warmblood! TB's and warmbloods cross beautifully!
And this is coming from a non-warmblood fan. I have nothing against them I'm just a Paint lover! Lol
But if you want to do well in dressage a warmblood is the way to go! If you want to keep the delicate confirmation stick with hanovarian type versus Oldeburg type
Good luck! :)