Your copper piece may be purposely patinated (oxidized) and if you do use a copper cleaner you will lose that patina.
Your shiny copper pieces will naturally patina. In fact it will have a different patina according to your own environment. You may prefer your signature patina, but if you want the shiny copper look, it is easy to bring it back.
We use Bar Keeper's Friend, which is usually available in your local grocery or big box store. It comes in powder, cream and liquid. We prefer the liquid.
Use a small amount and once the piece has regained its shine, wash it in soapy water and rinse very well. Then dry thoroughly.
The German silver is a copper alloy and also known as white brass. It rarely changes color, but may dull some. Just clean it in the same manner you clean copper.