With options to allow visitors to directly register to your website with or without requiring for an invitation code, Members Only [JomSocial™ Edition] is a Joomla plug-in that totally hides, every single page generated by Joomla, from unregistered visitors.
Visit the download link to see the full features list.
The program works just out-of-the-box, it is only needed to install the plugin (just like any other extension) and as soon as I published it, I had a private website.
Once I understood its Bootstrap template, it was a breeze to edit and customize it.
I must clarify that I can't rate tech support, because I haven't needed it yet.