A STB is a good choice, but yes, make sure you get one that has been re-educated. You want something that has an established canter, and try to get a trotter rather than a pacer.
What about a nice solid Aussie stock horse?
I would love a stock horse, to be honest. But I figured that when all I'm wanting is a plodder, it doesn't make sense to pay out the money required for one, especially when I have limited funds to start with.