Heh, should have answered my own questions:

[X] I want to join a corp for the socialising
[X] I want to join a corp in order to do mining in a group
[X] I want to join a corp for planetary interaction
[X] I want to join a corp, launch a POS, and get inventing and manufacturing
[X] I want to join a corp to trade
[X] I want to join a corp to run missions, exploration sites, and 'dungeons'
[X] I want to join a corp to explore wormholes
[X] I'll join a corp with my main character(s)
[X] I'll join a corp with alternate character(s)
[X] I'm mostly AFK when I'm on, don't bother me if I don't reply straightaway
[X] I'm willing to put up some ISK to run the corp (how much?)
10 M ISK
[X] I'm willing to invest time in the corp
[X] I'm willing to administer the corp
[X] I want to setup a corp to use my Corporation Management skills