Destrier, barded, and warhorse/large warhorse are my favorites. Courser works better for lancing since you just want to go in a straight line as you lance/couch. For 1H you need decent maneuver and a beefier horse since it will take damage as you charge through enemies. The bump damage on heavier horses is nice as well, since you will often find yourself cancelling a swing that won't hit.
Some of the 2H weapons with a shield might be easier for a weapon choice. More reach really helps. And nothing compares to the morningstar.