She's the leader of the brotherhood of evil mutants most of the time and when she's not that she's Nightcrawler's deadbeat mom who he hates.>>108054631
Cyclops and Storm are the leaders.
Wolverine is the loose canon who does what he thinks is right, everyone else be damned. Great character, but isn't the leader unless people force him to be, and every time he demonstrates why he shouldn't be the leader. He's the sort of character who has a strong personal code of ethics but little empathy.
Beast is actually more of an avengers character than an x-men character. When he is in x-men comics he's usually sobbing about how he's a mutant and being more of a fuckup than hank pym.