First: do not clean your coins! Cleaned coins almost always loose significant value over mint state, uncleaned coins. Only an experienced numismatist should clean coins, and only then if the current state of the coin is so bad that cleaning is assured to increase it’s appeal and value.
Do not store coins loosely in boxes, jars, drawers, etc. This will only cause the coins to scratch and dent each other and degrade their value.
If you must hold the coins, use cotton gloves or only hold them only by their edges. Finger prints and the oils of you hand can degrade a coin – both it’s appeal and value.
Do not scratch, polish, rub, or apply anything to a surface of a coin.
Do not drop or drag coins against hard surfaces. Consider getting a soft mat to work on when handling coins (velvet, cloth, or other soft surfaces work well.)
Keep coins away from moisture and humid areas. (Do not cough or sneeze near coins, this can actually leave marks!). Use silica gel to protect against humidity. Consider using a fire safe for storage and protection.
Store coins in original mint holders or use archival quality storage containers (NO PVC!). These containers can include 2″x2″ cardboard/mylar holders, Non-PVC clear holders, tubes, archival storage books — or send the coin in for grading from a reliable grading service (they will “slab” or encapsulate the coin for you).