1) Other (cost): The greatest sub in the world does me no good if I can't afford it. Since I'm putting together an HT system from the scratch, there are many other components competing for limited funds, so I want good value.
2) Responsiveness: The sub needs to sound good and blend in with the rest of the system. Otherwise, it'll stick out like a sore thumb and ruin the enjoyment of the rest of the system, in which case it might be better to not even have one.
3) Extension: The sub needs to go low, because that's the raison d'etre for the sub. Otherwise, I could just use the woofers on the floorstanding speakers, but where would be the fun in that?
4) Correction system: I don't know how my being-built HT room will sound, so it'd be nice if the sub could help things out. But that's less important than the items above because it could be compensated for with acoustic treatments or additional subs.
5) Aesthetics: It's less of a big of deal for me since the sub will be in a dedicated HT room. Plus, my wife has let the HT be "my room" (she gets to determine how the kitchen looks), so WAF is less important.
6) Size of box: It's the least important thing, as I'm willing to accept whatever size and shape the sub is as long as it sounds good (and doesn't cost too much).