To elaborate on what George said - for a Private Community - in edit mode you can set it to be Invite Only or Request to Join, and this can be changed back and forth anytime. You could do it either way. If you set it up as Invite Only, you'll need to invite the people you want to join it. People won't find it in search, and can't request to join it if they do or have the URL for it. If you make it Request to Join, it can be found in search (but no details can be seen, or posts in it), and people with the URL (like from your Share of it), can request to join, which you approve or not.