login to private pages

I am creating a simply site for my gaming clan members. There are some pages in which I only want existing clan members to have access to, not the general public. For now, I have made a page password protected, and placed links to the private pages within that landing page, and made all those pages private so no one can see them from the home page. However, I would like to keep track of all the members who are registering to view the secure pages, in case the private page password is leaked.

I have added a login widget to my sidebar, but all one needs to do is register and they get a password automatically sent to them. This is the AJAX login widget.

Ideally, I would like someone to register, and they are sent an email only AFTER I can approve them as an authorized user, and then they can access certain pages of the site.

Is this too complex for my simple site? Is it an all access or no access? Would I have to make 2 separate sites in order to have certain pages restricted, but other pages fully open to the public?

Any specific help on a plugin or widget that can do this, along with any helpful instructions is greatly appreciated. The site is:

https://www.beer30clan.com

Thanks!