I use a brewery-dedicated, toilet brush for keg cleaning. I use a plastic putty knife for helping to scrape off crusty stuff off of equipment (used to use an old credit card). I use only a soft sponge on everything else. I never use a scrubby pad or similar items, since they leave micro scratches in metal and plastic.
As for chemicals, I do use strong caustic and acids on occasion. But usually, I'm using something like the 5Star or Craftmeister products like PBW. For sanitation, I try and alternate between Iodophor and Starsan. Starsan doesn't kill mold spores, so its not ideal or universal, but I feel that Iodophor can leave a hint of a phenolic note in my beer if I use it without a complete dry-out.