Ron:
For everyday cleanups, I am very fond of the
blue Scotchbrite pads; they scrub and clean but don't scratch or polish.
The blue Scotchbrite is not the same as the green - the green is "guaranteed to scratch."
SOS or Brillo (or the dollar-store equivalent, which really are equivalent) are the right way to shine the inside of this cookware.
One tip about Club: Never store food of any kind in it. Anything with salt or acid in it (which is most food) will contribute to darkening and/or pitting of the interior. Put your leftovers in some other container, and wash the Club ASAP.
Also, don't put it in the dishwasher; this will etch the exterior over time. And dry it after use; don't leave it wet - this also contributes to darkening and roughening of the interior.
If something bakes onto the exterior, the blue Scotchbrite pads will generally coax it off. A bit of Bon Ami on the scrubber helps. If something really nasty builds up on the exterior, it's porcelain, so a spritz of oven cleaner will get it off, though you should be careful about getting the cleaner on the aluminum part.
Hey, Hans! If you're passing out Club, I'm looking for the ten-inch Stanish Omelet Pan.

I'll buy it from you if you ever run across one.