A brief overview of how my private playgroups work:
The classes last for approximately 30-45 minutes.
The groups meet the same day, same time for 4-12 weeks.
Rotating homes is fine, as is alternately one dedicated spot.
Groups tend to work a bit better when the age range of the kids is fairly similar - and we require at least 5 kids to start up.
There is no maximum amount of kids - it's more a commentary on the space available to us.
Current (active) groups get first priority in terms of time/day preferences when determining the schedule for each new session.