Building on Sibabrata's idea, I can see a way to approach this.
-Add all the modules to a page you could ever need for this purpose.
-Create a security role for each one named the same as the name of your module or module title
-Set the permissions of each module to be visible only to their like-named security role.
-Use a form generator module like Dynamic Forms to display your options such as "Featured List" in a drop-down list. Use the Dynamic Forms completion events to run stored procedures that assign the person to each of the security roles that represent the modules they have chosen to see.
Add another completion event that refreshes the page.

Note: the person will have to be logged in or you will have to get a module that automatically logs them in. There are a few that do that.

To do this idea, you will need to get a form generator like dynamic forms, another module that logs people in to the website, create the form, create some stored procedures and tie it all together.