There's nothing like your first!!!!
Essentially here is the cleaning rule - don't!!!!
That rule applies only to key date or very rare coins. Other's, like your merc, are cool finds, but really only worth their melt value so as far as cleaning, have at it!
Baking soda, baking soda/salt, w/aluminum foil and boiling water, electrolysis, and tumbling all good ways to clean dirty coins. With the exception of electrolysis, you really can't hurt them. Electrolysis can melt them, shows up as pitting.