Baking soda is a gentle yet but semi abrasive must for your cleaning supplies. I use for cleaning toilets, making a soft scrub for grout, as an odder remover. Read Simple Cleaning Tips Part 2 for more ideas.
Hydrogen Peroxide is great stain remover. My top uses for it are removing spots from carpets and fresh blood stains on cloths. Replace the cap with a spray nozzle and you are good to go! Spray on stains and let sit for 5 minutes before trying to scrub or rinse them out.
My favorite dish soap is BioKleen. I like that is a safe, natural soap since you spend so much time washing dishes. I use it in my 3-in-1 All Purpose Cleaner. I even use it to wash my car!