The most standard opens in bughouse are e4/e5 and d4/d5 now.
In the past, standard was e4/d4 vs e6 setups with black either playing d6, d5, or bringing our 2 knights and a bishop next. This turned out to be overly defensive by black as far as pawn structure, while Bc4-f7 sacrifice vs 1...e5 isn't actually very good (but seems good when players are newer).
Note that in e6/nf6/nc6/bb4 openings, or 1...nf6, or various others, it's pretty common for black to play aggressively and sacrifice material (especially if white is over extending). White isn't necessarily the aggressor and has no easy to to quickly punish e6 openings. White normally would get a good position with center control then apply pressure and try to win more slowly.