Common watch crystal types include sapphire, mineral, and plastic. The sapphire ones generally offer the best scratch resistance, but at a somewhat high cost, while plastic (acrylic) and mineral offer less scratch resistance. Since the crystal covers the face of the watch and is very visable and often impacts objects, it’s important that it not be easily scratched. So in general it’s best to try to get a watch crystal of type sapphire or synthetic sapphire.

Whether one should try polishing watch crystal or not largely depends on the type of crystal the watch has. If the watch face is acrylic, then yes, polishing with polishing compounds can often help. However, if the watch face is sapphire or mineral crystal then it will probably not be possible to polish it yourself without access to specialized equipment. Replacement may be the best option in those cases.