i believe the top tier horses are: kentucky Saddler, American Standard Bred, and Hungarian Half Bred.
if i remember correctly, the KS is the most well rounded horse both in terms of speed and stamina, while AS is the fastest but with the lowest stamina and HH is the slowest of the 3 but with the most stamina (pls correct me if i am wrong guys).
additionally, there's also a dark horse that you get if your fame/honor level is low (not sure how low), but from what i've read, it is neither faster nor more durable than the top tier horses.
supposedly the war horse is the best horse, but since its only available with a certain copy of the game, the abovementioned three horses are the ones that i stick with (tho i haven't gotten the AS yet).
Breaking in and hitching the 3 fastest horses excluding the War Horse gets you a trophy, but i'm not sure if it increases your total %. I have all 3, but never bothered to check and see if it rose my % at the time.