The cleaning approach here depends on the tub's material. Enamel-finished steel or cast iron tubs are generally quite durable; those made of fiberglass or acrylics tend to scratch easily, and anything that has been scratched becomes progressively harder to keep clean.
Bon Ami, or a white scrubbing pad treated with detergent, will clean the no-slip surface treatment at the bottom of the tub; if soil persists, try baking soda and water with the pad.
Instead of buying a lot of expensive cleaners made for these surfaces, make a poultice of laundry detergent and water, which will attack hard-water stains as well as soap scum. Rinse well and dry to prevent formation of new water rings.
Avoid using heavily abrasive cleaners or pads on these surfaces, and don’t use acetone or other strong solvents on fiberglass or acrylics. Solvents can break down the plastics used in these tubs.
Reference:
Consumer Reports editors in How to Clean and Care for Practically Anything.