I've recently updated and found that Unity shows on the gnome-classic/fallback desktop. Is this a new feature (which I doubt to be), or a bug? If it is a bug, tell me how to disable Unity because it interferes with the lower panel (i.e. I bring out Trash instead of showing the desktop when I try pressing the "Show desktop" button when the panel is not in focus).
I don't encounter this problem in gnome-classic (No effects).
Don't judge me. I like pokemon!
The difference between Gnome Classic and Gnome Classic (no effects) is that the former runs Compiz. It seems Compiz has a Unity plugin, which if enabled, will bring forth that panel and menubar that is annoying you. See this link I found on the Ubuntu forums. The poster there used CCSM to disable the plugin. I don't know if that's the best way (CCSM doesn't have a great reputation, to say the least). You can search this site for alternatives to using CCSM.
Maybe you have gnome-panel installed
You can uninstall gnome-panel to remove the gnome panel in the bottom!
On the login screen you will observe a small icon next to your name. Click it and select the appropriate desktop environment setting.
