Rock band is a good game for their start, the only downside is the drums utterly suck, nothing that it comes with is built to last except the microphone maybe.
Guitar Hero 3 is good overall, the controllers don't break as easily if you don't do something stupid with it, the game is awesome, the only bad thing is it's too easy if you're experienced at it, which since you're buying it shouldn't be a problem.
Left handedness wouldn't affect your gameplay, they have different setting for it.