What to use: Any high-quality (non-abrasive) furniture/guitar/drum polish/wax should give excellent results on lacquered and covered finishes. Trick Cleaner "wipes" are easy to use and an excellent alternative to spray on cleaners.
It's not necessary but it's recommended that you remove the hardware from the shells to make cleaning faster, easier, and more thorough because you don't have to navigate around the hardware. Removing the hardware also reduces the risk of scratching the finish from grit that accumulates around the hardware. Remove dust from the shells using a feather or "Swiffer" type duster.
Use a soft clean cloth for cleaning/polishing - microfiber cloths are ideal. Don't use paper towels as they are too abrasive. Apply the polish/wax then carefully wipe it off turning the cloth over frequently. It's easier and more thorough to polish the hardware before reattaching them. To prevent unnecessary nicks in wood bass drum hoops, position the claws exactly in the same spot before they were removed.
Most acrylics can be cleaned with a soft, dust-free, damp cloth. Many acrylic drum collectors recommend staying away from household glass cleaners (i.e. “Windex” and other glass cleaners,) as they do not lubricate as they clean. Dust and dirt trapped between the cloth and surface can leave super-fine scratches that can, over time, diminish transparent shell clarity. Products like Meguiar’s Mirror Glaze and Novus Plastic Clean and Shine are recommended by most collectors and interior design professionals for regular, scratch free cleaning and scratch removal from acrylics.