Group Registration

I have a camp for teenagers planned in July. When they pay (offline, cash) I wonder if it’s possible to do the following:

1) They would go to a page (or something else) and see 4 groups there
2) They would see a list of who’s currently in the group
3) They would choose 1 of 4 groups and will be added to the group

They all have WordPress account but it doesn’t have to be WP registration.
Is there a plugin that would do that?
Or is there anything online that would do the trick – free or paid? (it can be something outside of WP that can be linked to it – like PHPBB).
Or may be some coding…?

I tried BuddyPress – it will not work – it’s too abstract and not very visual and simple.

Any suggestions would be appreciated
Thank you!