When Should You Do It

The answer is pretty much never. Old coins have a patina and removing it generally lowers their resale value.  If the coins are flithy, the only cleaning you can really consider is weak detergent (soap and water) and rub between fingers.

There is often chlorine residue, salts  and other contaminants  in tap water. Gently swirl coins around in distilled water, to rinse them is a good option. Please only do this one coin at a time.

Pat, rather than rub, with paper towels until dry. Make sure all coins are absolutely bone dry before storing or displaying them.