To remove soap scum, you need something acidic like Stonetech "Revitalizer. " But some problems need an alkaline cleaner like Stonetech "Heavy Duty Alkaline Cleaner. " If your shower is a natural calcite stone such as travertine, do NOT use an acidic cleaner. It will etch the stone.
I recommend the cleanser Comet for cleaning shower floor tile. Dampen the shower floor and then sprinkle Comet powder on it and let it soak for a few minutes. Then use a scrub brush to clean away the dirt and grime.
I would recommend using a product you can find at your local dollar store called "Awesome". This all-purpose cleaner is very effective in removing soap scum, as well as anything that sticks to the tile or grout. Everyday hydrogen-peroxide is very effective in killing mold if you are concerned about using toxic household chemicals.