personally i love the sound of a live set (everyone playing together), but that also take 1) a lot of mics 2) a lot of takes 3) a lot of isolation and 4) a lot of practice. and generally u wont be satisfied with the sound ;o.
as for doing it individually, it kinda depends on the band. if the band is tight, ill record the drums, then bass, then guitars, then vocals. if the band is sloppy, ill usually try to find the tightest player (either guitar, bass, or drums) record a scratch track, and go from there, DESPERATELY trying to find the best take for each player. sloppy players r the worst to work with, so thats usually takes a LOT longer than a tight band. if they dont have ANY tight players (they'll usually say they're used to playing together -_-), then setup a click track and have someone do a scratch track to it and hope the rest of the players can adapt to it.
ive actually had a band that only knew that song by what the vocalist did at one point. so they had no idea when to go into the chorus and verse and so forth, cuz the vocalist would usually do something to trigger that. i had to record a scratch track of the guitar w/ the vocalist singing, then do that for the bass, and had the drummer essentially "LEARN" the song in the studio. it was pathetic, but i got more money outta it so i cant complain -_-. anyways good luck recording and if u have any other questions, this forum is VERY helpful and the people here are more than welcome to help u out