Question About Making Site Available

I want to make a site available to new members who sign up. Each person would get their own space upon joining that would be based on a similar theme. They could customize some areas like background, header and profile image. Menu items and other areas would be managed by me.

My question is how do I make this site available to new users once I’ve built it? How would they get access to their own version of the site? Is there a particular plugin or program I need to pull this off?

Thanks in advance for your help!