Over the years I’ve had many tales of woe from people who have spoiled the surface of their bath through too-rough cleaning.
If yours is acrylic, use an all-purpose bathroom cleaner (never anything abrasive). Any scratches can be very gently rubbed with cream metal polish.
If the bath is enamel, use products only with the Vitreous Enamel Association logo on the back label.
Never, never throw on limescale remover – you will strip the top layer of the bath.
If you’re unsure of anything, test on a small area first.