word! About the buzz, most of the time thats a shielding problem, or occasionally an earthing problem. Ive fought with that a couple of times.
Pa**ive or Active? Depends on your budget. A good Pa**ive set of monitors coupled with a matchingly great amplifier will cost a lot more than equally sounding actives. Actives are also easier to transport and you need not worry about what amplifier to use, u just give them a good signal and you game.
And eish, i would stay away from Alesis, rather go for KRK. But in the end its your ears, with your room, with your speakers that determine final result.
Shallom!