What's the best cloth material for simply wiping away fingerprints and smudges on the frame?

Microfiber, same as your car.

I use Costco microfibers, because I have a gigantic bag of them. Spray bottle full of Optimum No Rinse, which will undoubtedly outlast my bikes, and me as well (the bottle of concentrate makes 16 gallons.)

I use old cotton t-shirts, since I have way more of them than I need.