Cooperman-built drums and REMO drum heads are a great pairing - durable, and powerful sounding. They are built to give you many years great service, and they are really quite easy to maintain and keep clean. 
Since the early days of the pandemic, we have been following a protocol of lightly misting a soft cloth with an alcohol based sanitizer, and then using the cloth to wipe down the drums just prior boxing for shipment. The drum finish holds up well to this, and continuing this routine is a best-practices way to keep your drum clean.
Our shells are made “ from tree to finished drum” at our millshop in the foothills of Vermont’s Green Mountains. Local hardwoods - primarily Ash, Cherry, or Maple - are sourced locally, dimensioned, steam bent, and finely sanded by a small team of seasoned drum builders. The finished drums are top-coated with a musical grade lacquer, lightly scuffed, and, finally, we apply a thin coat of paste wax, again bufffing to a soft feel and burnish. The lacquer and wax give our drums a classic, soft, warm luster. In time, the wood darkens some, developing a distinctive patina. You can clean any accumulated dirt by wiping the shell down with mild soap. To bring back the luster, you simply apply another thin coat of wax and polish it out with a soft cloth. We have , for years and years, used a New England carpenter’s standard - Butchers Brand amber Boston polish. MInwax makes a similar wax that may be easier to find in your local hardware store. Waxing serves to both polish and clean the wood surface.
If the drum is badly scratched or damaged - or unexpectedly painted on - you can return it to us at any time for repairs, refinishing, or a general overhaul. 
Check for dirt and debris accumulating on the inside of the drum, especially at the margin where the drum head material makes contact with tuning ring/shell. Use a damp soft cloth to clean in that tight spot. An alcohol based cleaning wipe could be used. Alternatively, you could use compressed air; many people have this at home as a spray can that is used for cleaning a computer keyboards - don’t forget to wear safety glasses!
As for the drum head material, Cooperman uses, exclusively, REMO brand synthetic drum heads. There are a number of different formulations of the materials, but they are all Mylar, which is extremely durable ( it’s meant to be struck, after all) . We recommend cleaning with mild soap and water. 
If necessary, you should feel comfortable using any readily available household cleaner like Windex, 409, etc.. For the most stubborn inks , you could, sparingly, apply a more potent solvent based cleaner - something commercially available at your local hardware store, like acetone or lacquer thinner - to a cloth and try to rub out the ink. Always follow the instructions provided by the manufacturer, and please be mindful and cautious when using these kinds of chemical products.
All in all, the drums are super easy to keep clean, and that’s all the better so you are free to focus on playing and sharing the rhythm.
