"Portal Bar" sounds excellent.
I placed it in the theme's header.html page so it ends up appearing on all the pages. I tend to like that, but some might only want the bar to show on the home page.
At the actual site at http://advertisite.us/missions_training/, the Portal Bar actually connects to four different websites. The first link on the left "MissionaryNet Main" could be likened to a "Home" button because my main website and my moosle site on on different servers (a long story). Another button links to Moodle and three connect to other php scripts I use on the site (classifieds, contact, and newsletter). An option for something like student's links would be adding yet another script like phplinks.
It isn't a true integration as each of the different scripts requires its own passwords, but most of them are only for support issues antway and don't get used that often.