Creating a folder structure

I don’t think what you want is URL rewriting. If I understand correctly, what you want is to restrict access to certain pages, posts, categories, etc., based on the current user’s role or capabilities:

“If logged in, do something. If not, do something else (like prompt to
login or register).”

Modifying the output/behavior of a single page is not all that difficult. Just use the is_user_logged_in() function to check the current user’s status.

<?php 
    if ( is_user_logged_in() ) { 
        // Show your "logged in" user content here.
    } else{
        // Show your register/log in form here.
    }
?>

However, if what you want is TRULY a Member area, with multiple pages and sub-pages, I would consider using a plugin to accomplish this. In addition to the plugins offered in this solution, you might also want to check out Role Scoper. WordPress lists a few of these options as Resources on their Roles and Capabilities page.

Simply create a page called “Premium” (for your specific case) and use one of these plugins (or something similar) to set restrictions for that page and every page beneath it. You could use a custom template for that page to determine what functionality it includes.