For me it would be music first.
Then, well it occured to me that the place where you reside will also be a factor for most people. The quality and frequency of fan interaction will matter most to the ones who can regularly attend these events, and much less so to foreigners I would think. This is probably at the bottom of my list but it still matters.
Great lives is pretty big, even if I can't attend them. I can still watch them on dvd or online.
Also, their online presence. If they're pretty active on twitter, FB, YouTube, then it makes following the group even more enjoyable.
Edit:
Oh, uh yeah. If one or more is cute it kinda helps.