Knoppix comes with KDE, XFCE, icewm & a couple of others but not Gnome. However, I gree that Debian/apt-get is the easiest way to install things. Like you, I have greyed more than a few hairs trying to install things on Mandrake...in my case trying to upgrade MDK 9.2 to KDE 3.2. Which is one of the big reasons I'm back with Knoppix, it's one of the easiest ways to get a Debian system install.
Put your left leg out, hokey-pokey, you should be able to install Gnome without much problem. You will have to modify a few xsession startup scripts to get away from having Knoppix use KDE but that shouldn't be too hard & there are lots of willing non-KDE users here to help you out.