The first thing you need to know about polishing metals is that the compounds used are abrasive. That means they remove material as they polish. You will expose the base metal and ruin the piece in an instant. The best you can do with these is to use a chemically treated cloth. With solid precious metals, you still need to use a great deal of care.
New jewelry is one thing to work with.
A worn piece may have several thin areas and can be seriously damaged. A well worn ring band can develop sharp edges in a matter of seconds. This can be severe enough you will need to put a new shank on the customers ring. Worn prongs are another problem area. You can quickly remove enough metal that they will need replacing.