I collect all pre-1982 pennies out of my change. Some 1982 are copper, but I don't fool with them as earlier ones are easy to come by to be positive you're getting copper.
I soak them in a bath of vinegar and salt (glass bowl only) for about 30 seconds. Don't leave them in there too long, just enough to get clean. I stand there and stir mine around a bit to make sure they all get the gunk off.
After rinsing them, I make a paste using baking soda and vinegar and scrub them with a toothbrush. Rinse, and your pennies will look fresh from the mint.
Do all this prior to pressing. It doesn't really work, for some reason, after pressing.