It really depends on your situation. The pros and cons of each are explained below, which should help you to better make a decision:
If you use your mixer or audio interface with multiple microphone ports, the only issue is that it will all be recorded onto a single track in Zencastr. It isn't able to record separate channels from a mixer yet as the browsers aren't equipped with that feature. If you need to edit the track, it may be more tricky to do it with all of the voices on a single track.
A mixer like this will do the trick and isn't too pricey:
If you have everyone on different computers, you will all have separate tracks which will make editing easier. This depends on your needs though. That means one person will be the host and the others will receive the guest link for Zencastr.
The only issue with everyone recording in the same room on separate computers/laptops is that there may be audio leakage problems where each persons mic may pick up the other people in the room. There is an option when you run a Automatic Postproduction (mixes the tracks together) called Cross Gate that will try to remove the other voices but we're not sure how well it would work in this case. I would definitely do a test run before you try and record a full show.
See our article on the Cross Gate setting.
A not so ideal solution would be to have each person in separate rooms to make sure that each persons microphone only picks up their own voice.
If you need further help, please contact support.