When I create a user account with authenticated user permissions + some additional create/edit permissions, the Drupal Menu-bar or the CiviCRM menu-bar doesn't show. Only when I add the admin privileges to the user account, do I see the menu bar. So how is a non-admin person supposed to navigate between the various modules (contact/ membership/ event/ contribution etc.) without having full admin rights? Am I missing something? Thank you for your help.
One option would be to create a Menu Block or just a Block with some links and set it in to a region with settings so it only shows for Authenticated
But also, am unclear if you really want a non-admin person getting to those 'modules'.
If a non-admin person is making donations, registering for events they do not need access to CiviCRM itself.
Perhaps update your Q with more detail about what the non-admin person needs to access perhaps by providing the paths you want them to get to so you avoid saying 'member page' which could be construed in many ways. HTH