Fencing Pages with Registration

[ Moderator note: moved to Fixing WordPress. ]

I’m new to WordPress so I’m not really even sure of the terms to search for. Here’s what I’m trying to do. I’m helping a friend set up a WP website that has unsecured areas (always accessible) but also areas that should not be accessible unless you “register”. Once registered, a particular page or set of pages is accessible. Registration will include details such as name, email address, and phone number. It should allow me to keep copies of the registration information for future contact. The user will also be able to log-in later on during subsequent sessions.

Are there any plugins that can do this? I’ve searched but I can’t seem to find what I want. I may not be using the right terms.

Thank you