You can create custom menus, thats not a problem,
Then you can create a module for menu in Admin->Modules, then choose to show that menu only for a specific group.
Once you have your menu sorted out and you changed Login-box to show for the anonymous group, goto Admin->general and clear the show modules for all groups check.
I use something similar on http://www.damosoft.co.uk so that I can have online projects (different sections and forums) visisble for different clients.
Hope it helps you, if you want more info, just shout be back.