Because cheeses are living organisms they need the careful balance of making sure that they are not cut off from air, but also not drying out. The best way to accomplish this is to use waxed paper or aluminum foil. Plastic wrap is ok as well since it is more common to use but you need to make sure to consistently rewrap theses cheeses. Plastic wrap is more ideal for harder cheeses. The best place to store your cheeses is in the vegetable drawer of your refrigerator. It is slightly warmer than other areas, has a nice level of humidity, and is away from other foods that might release some odors that the cheeses can potentially pick up.
Never freeze cheese.
If mold should appear on fresh cheeses or should the cheeses become slimy, throw them out. If spots of mold appear on other types of cheeses simply scrape them off and cut around the spot and the cheese should be fine.