Creating open content area and restricted content area

Is this something that WordPress is capable of or should I search for
more complex content management systems for solution?

The two sections should be easy. Create a Custom Post Type for either your free or your paid content. It would be easy to restrict the one or the other by checking (is_user_logged_in) to see if a user is logged in before displaying content.

WordPress does not have a built is payment system but there are numerous plugins for many of the third party processing companies.