#2
Economy picking is a kind of middle ground between sweep picking an alternate picking.

That is, alternate picking is picking up and down strictly, whereas economy picking is always picking in the direction that will get you to your destination as fast as possible, but uses alternate picking as a basis.
Quote by marmoseti
Mastering your instrument is being able to play whatever you hear in your head, unhindered by inadequate technique. After that, it's all about what you've got to say, so there would be no "best," just a bunch of people saying exactly what they mean.
#3
alternate picking- down up down up pattern, no matter what.
economy picking-basically think of it as going the shortest possible distance to get to the next note. if you are going from lower to higher strings, go down down etc., higher to lower strings up up etc. staying on the same string you just stick with alternate picking, up down up down.

each has it's own pros and cons. i prefer economy picking.

edit:there's a good article about it on ug somewhere...
#4
Alt picking is strict ^ V ^ V picking so up down up down even when switching strings.

Econopicking is similar, but when you switch strings you pick towards it. Say you were picking G string 4 times than moving to the D string 4, you would go V ^ V ^ ^ V ^ V so that way you pick up on the last G string note then up on the first D string note as well since you are moving in that direction already. This cuts down on extra movement.