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.
Fees have another effect on a group.
People who are paying cash tend to take the work more seriously. If a member is really committed to the art they'll pay for the schooling. Where there's commitment, you'll find professional level talent. If you're forming a group, it's absolutely essential to know how to do constructive criticism. You may think you do.