If You are cleaning them just for 'fun' and they have no real value - be careful some 2p coins are worth a bit more than you would expect - then, in my experementing, Silver Dip will bring up a copper coin to a nice pink finish, but that will last and never return to the correct copper colour. Beware of stripping the copper plated steel recent versions, you can tell these with a magnet. ABOVE ALL Check the rareity of everything before you do anything to the coin
To a point I agree the warm soapy water theory, but drying it will rub the high points and leaving it to dry naturally will leave a film over the fields, and these can be spotted and reduce the value. So, wash them in water after? Yes, but only soft water, never hard water the question then is how do you dry the?. Never rub, that will wear the high points and leave scratches in the fields. Leave to dry natyrally, not really there will be marks and you will need to stand the coin on its edge. Heat, no similar problem with marks and may affect the fields of the copper.
It's a right puzzle - best not to touch them.
The bigger issue is the decision about a proof coin with a finger mark on it. clean or leave ?