Jewellers rouge is for putting the final polish onto gold and silver. It is also used in the windscreen industry for removing fine scratches, and so should be suitable for glass windows, shop counters etc. It is very cheap, its only drawback is that it's messy (it's the same compound used in makeup to redden the face). We also have a selection of 'clean' compounds for polishing metals (anything from heavy railings to fine neckchains) as used in professional workshops.
For very soft materials use our 'scratch remover', it's much finer, better for plastics including acrylic watch 'crystals'.
Polishing mops fit onto a polishing motor (or we sell an adaptor to use with a hand drill) and are used with polishes (jewellers polishing compounds). A simpler method, for small easy flat-ish items, is to use a succession of polishing sticks, each with a finer grade - these are good for removinig the stain caused by testing acid.