I use sponges and paper towels.
1) Sponges to scrub stuck bits off of the surface.
2) Wipe down said surface with paper towel to remove most moisture.
3) Thoroughly wash hands.
4) Clean surface with cleaning agent (current choice is Lysol Kitchen Pro) and paper towels.
I also keep Clorox Anywhere handy for quick sanitizing of surfaces that have been used but show no visible soiling. My Choice. You don't have to agree.
I choose paper towels for the same reason that CA retail health codes require single use towels at hand-washing sinks, eliminates towels as a possible source of cross-contamination.