The one thing I look for in an FC is one that participates in the same level of content I want to do and actively throws up invitations to members, regardless if they know how to clear the said fight (assuming they're showing interest in learning).

for example, my FC:

leader: "hey anyone wanna come clear Titania ex"
player: "i havent got past phase x"
leader: "dont worry about it, come anyway"

Our whole FC teaches one another and its a pretty great thing. On weekends, we sub for each others statics to help people get their weekly clear. I guess my point is that an FC that fosters a culture of helping one another get through tough content really forges a bond (it did for me at least) and now I never want to leave.