Anarchistic and democratic groups tend to be ineffective unless the membership happens to be extraordinarily disciplined. The leader needn't be a published author, but an authority the members respect. Someone who is capable of keeping things running smoothly and restricts criticism to the technical merits of a writer's work, not the subject material addressed in the piece. The leader's most important trait will be their ability to maintain group cohesiveness. Optimally they should have a broad acceptance of writing genres.
Diversity is healthy and educational.
As important as the leader, is a membership of differing skill levels. At least one person should be experienced, otherwise it's simply the blind leading the blind. Remember, education does not necessarily take the place of experience. Experience is knowing fiction writing, how to critique it, how to make it better. If you're building a group and don't have a qualified person to run the collective, consider charging show-up dues and enticing a local author into running your group by paying them from the weekly collections.