Go to your sporting goods store and try bows out. I'm not sure if draw weight is actually that much of an issue, unless you mean that it needs to be light in order to shoot fast. In any case, that's a general rule. But, for the type of shooting done in the videos, the bow needs to be of the type used by light cavalry (such as the Mongols or Apaches), not the long bows with heavy draws used by foot soldiers (like the English longbow). The heavy longbows were used for distance shooting, not accuracy.
The Robin Hood references were interesting. I think his argument against quivers a la Hollywood is spot on, but it's doubtful that archers ran through the forests shooting arrows at each other the way that cowboys used six-shooters in the old West. Arrows are easily deflected in the woods. It doesn't matter how accurate you are if there's something in the way. Ask any bow hunter. It takes being close, quiet and clear.
Anyway, I think a person could start training with any conventional short bow that is possible to draw, even a kiddie bow. Compound bows are compact, and the pulley system makes for a light draw; but they're probably too complicated to practice the real skills. Imo, the hardest part of what Anderson does is holding multiple arrows and accurately nocking each of them quickly.
I tried to find some clear pictures of Apache using bows from horseback. Here's one of buffalo hunting, and the bow size is clear. It's not so clear which side of the bow is used or where the arrows are held. Apaches didn't need to hold onto reins.
Btw, Apaches and other Amerindians did use quivers.
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