The best thing to do is use pre 1982 pennies, you can clean them in a number of different ways, one way is to soak them in vinegar, or you can use braso to clean them, newer pennies are not solid copper and can leave a nickel smear in the design.
You don't want new pennies because they have zinc in them that will cause a silver colored smear on you pressed penny. You're looking for pennies that were minted before 1982.
I've read online that you can actually clean pennies with, now I'm not making this up, Taco Bell Hot Sauce (yes, the stuff in the packets). It's the acid. You can also use vinegar or lemon juice (both acids). Good luck.