I never use boots. Unless your horse interferes, or you're jumping big solid obstacles (cross-country) you really shouldn't need them. I had a Dressage trainer insist on TIGHTLY wrapped polo wraps
on all horses. I asked and asked and asked about WHY he had this policy, even though it's been proven that polo wraps (and most other "sport" boots
) don't provide any real "support" the leg and he never could come up with anything, lol. I used them the first few lessons, then quit. They were a PITA to clean and keep rolled up. He'd gripe at me and scold me in front of the other students, so I'd just flip him off as I entered the ring, lol. He still took my money and gave me great lessons, though I think he enjoyed yelling at me more than his other students...
ANYHOW! Back to the subject. Plain split or galloping boots
are just fine for protecting the lower leg from the occassional knock. You don't need anything fancier.