Hello everyone. I have two questions regarding warfare from horseback. First, what length of sword would be required to effectively fight from horseback? Does grip length matter here? Secondly, what type of shield would be used from horseback and would this affect a horseman's ability to shoot projectiles (bows/crossbows) from his horse? Thanks for your comments.

It also depends on when we're talking about. For example, a late 11th century Norman circa the First Crusade would probably have something like a Oakshott type X, but by the time of the third Crusade, maybe something trending to be a little longer like a type XI. One-handers would probably be most common through most of the Middle Ages, but longer hilts certainly wern't excluded.
Kite shields and later "heaters" would probably be the best bets, but again, it varies with what time (and where). Not sure about mountd archers, but my guess would be they would: a) wear a "normal" shield on their back via a guige, b) use a small shield so not to get in the way, or c) use no shield at all.