If something with good loot is being fought, then random looting is best. For most looting, Free For All with the rule of don't be greedy seems best. Random on the good things is also a nice idea. Alpha loot and the like involve someone keeping track of whose turn it is, and I have yet to meet someone who can do that well for extended periods of time. Generally tanks lead.
Tanks are the best leaders.
Warrior-types most often. I feel that tank types who will be pullers tend to have a better overview of how a battle should go, and, unless someone else has a lot of experience in the area where we are hunting, I look to them to lead. I am a very open, vocal person, therefor, I usually initiate a group and just start inviting the people to join me when we all meet up. No, it is the person behind the character, I play a monk, rogue, druid, cleric, bard, SK, enchanter and have played them all to 50, and I have always lead the group. No, usually a personality type.