The general idea is that you would create an event for each meeting. For each event, you would create a a signup schedule, and an Event Synopsis containing the meeting agenda. The signup schedule might be as simple as a single activity named Plan to Attend (or the like). Then in the future, you would use Search People or Output Report to display who attended when.
Because this is a recurning meeting, we suggest you check the Repeats Frequently box when you create the event for the 1st meeting. This will facilitate bookkeeping for your meetings (as described
here). In particular, it makes it easy to clone a later meeting from an earlier meeting and to setup a reminder for when this should be done.
Let's also suppose you want to allow people to plan up to 2 months ahead. Therefore after you have fully setup the 1st meeting, immediately click on create next one and fully setup your 2nd meeting as well. When you get the reminder mentioned in the previous paragraph, you should create the 3rd meeting — and so on for each successive reminder/meeting.
Managing meetings this way pays off the most for large meetings or when there are jobs beyond merely planning to attend. For example, maybe you need volunteers for reserving a room, getting refreshments, writing the agenda, being a speaker, and so on. If so, you would add these things to your signup schedule. Also if you need to keep track of who planned to attend and did not come, you can mark No Show on such signups.