There are many factors that affect the arrows you use.
Your budget, your horse, your build (HA and WPP) and most importantly how accurate YOU are.
Also, there is no way around it, your damage will suck which ever arrows you use.
For max damage agaisnt the target you actually have a chance of killing, Tatar.
Barbed are great though, nice bonus, specially if loomed, larger amount of arrows and very easy to upkeep (very important if you like expensive horses such as courser/destrier/arabian)
Bodkins are for plate and expensive.
"Arrows" are great if money is short, and a good HA will do well with them anyway...the amounts of shots taken to kill no plate with better arrows can be 1 shot difference in many cases.
A word of advice though, forget looming arrows for now, loom the bow to x3, loom the horse to x3 and then loom your arrows.