Well it kinda depends what you count as "hard hitting" cav. As in str will give you higher ps + bigger base damage, but agi gives you more riding and thus more acceleration, manouver and
speed and speed always gives you more damage. There is no simple answer to that question. If you want to 1 hit people you also
need to actually hit the target, which might be difficult with low riding builds. Still if you don't hit the head you will most likely have to take another turn and hit him once more even if you have high strength.
I use heavy lance and arabian/courser. Some cheaper horses are fine too if you know how to use them. Desert horse and Rouncey are good low cost horses. I don't like normal lance. Light lance is better in my opinion of the other two ;)
EDIT: Sidearm could be basically anything. Depends on if you want to take a shield or not. Without shield you can take some 2slot polearm that you'll use once you get dismounted (good thing is that you don't have to split your wpf. Just the way I like it. You might like some 1h proficiency for example? You have to decide yourself)
Couple guides:
Builds and stuff
http://forum.meleegaming.com/guides/(guide)-toffi's-cavalry-guide-(big-update)/Tactics, that make you a hard hitting cav (build is irrelevant)
http://forum.meleegaming.com/guides/(guide)-son-of-odin's-cav-guide-(lancer)/Kill
