For removing grease stains: David Burke, executive chef of davidburke & donatella, in New York City, recommends "baking" stainless pans at 400° F for two to three hours (be sure the handle is ovensafe). Remove the pan with a pot holder (it's going to be very hot), rest it on the stovetop, and flake off the grease with a spatula.
For safe storage: Burke keeps his best copper pots in the drawstring felt bags that come with good shoes. "That way they don't bang around and get scratched, and they don't get dusty," he says.
To clean copper cookware: Christopher Kimball, editor of Cook's Illustrated, recommends smearing a thin layer of ketchup over a tarnished surface with a paper towel. Wait five minutes before rinsing it off.