One matter that needs to be settled in every writing group is how to decide who to critique first each week. I once had a group who decided this by a round of rock, paper, scissors. The game could go on for five or six rounds sometimes, before we had an actual winner. Some people enjoyed this. I did not.
Another group critiqued in order of arrival. That worked well when we weren’t meeting at anyone’s house, because no one was necessarily first. That same group once chose according to whose birth date was closest to the current date. A skype group I was in chose based on whose submission was up on a certain group member’s screen when it was time to start.
By far my favorite method, though, is the one used in my current group. We roll a scatter die.
The arrow points to the first person, and then we proceed clockwise. Simple, quick, fair and we get to roll a die. Can’t ask for better than that.