I don't think we can haggle horse prices in the vanilla game. Edit: In fact, I know we can't.
On topic: I don't think there is a 'best'. Even paint horses (being the slowest) have the advantage of better manueverability if we're in an area with lots of twists & turns. Black horses may be the fastest in a straight line, but it's difficult 'steering' one in a heavily-forested area (or an area with lots of boulders) without constantly running into things.
If you are having trouble keeping your horses alive, best thing to do is make sure if you are trying to fight an enemy that you ride far past this enemy. Dismount. Get off and run towards the enemy. What usually happens if you don't do this is the enemy will attack your horse instead of you. If you get to the enemy first, the enemy will usually focus on you instead.