I dunno, I think your way is right. When I see people playing fast, it is a small motion of the forearm, not the wrist. The wrist has to make a big motion, cause it can't just cross the strong, has to go vertical too u know? Circular motion, that's bad. I've heard some say the actual picking motion comes from the wrist, whereas moving between strings comes from elbow. With me I just pick from elbow and do fine, i find you can just get way faster that way.
Are you gonna trust Kirk Hammet about picking? I've never heard him pick a fast run, he's all legato like his teacher satriani (who blows him away imho, but that's a different discussion.) Different people will tell u different things, but look at somebody good play and I think you'll see most of the motion from the elbow.
As for my pick, I mostly use a jim dunlop 1mm nylon, but I'm not too picky, I'll use the 3mm stubby jazz picks, those are thick mofos. I find that if I angle the pick just a bit, so I'm not picking totally parallel to the strings, the pick glides off the string more, there's less of a clicky click attack, and its easier to get faster cause there's less resistance.