The plastic that the clay comes in:
When you open the package of raw clay, Try your best to open it neatly. I used to just tear in a brand new package of clay and not mind the plastic packaging. Instead of ruining the packaging,open it neatly and then use a piece of tape to close it afterwards.
This is the easiest and cheapest way to store your clay and make sure it is not prone to touching other raw or baked clay. Along with keeping it sealed, this avoids it touching other surfaces that it can ruin or leech(paper or cardboard boxes) into. Some plastics can react to raw polymer clay and cause the plastic to be eaten away and damaged.
What if i ruined the plastic packaging the clay comes in?
Raw polymer clay can be stored in Wax Paper or Parchment Paper. I personally prefer Parchment Paper, you can bake on it without getting shiny spots on your clay.
Plastic Wrap/Saran Wrap/Plastic sandwich bags. You can store your clay in most types of plastic wrap or sandwich bags.
Plastic warp and zip lock bags are my preferred method of storing clay. This keeps any dust or lint out of the clay while in storage and you can easily see what color is in the bag.
I also like to put plastic wrap over my raw pieces of clay that i am currently working on to protect it from dust or lint.
You can also store your clay in plastic boxes/ tupperware. However, before you store your clay in plastic, inspect the packaging for a few numbers. Types of plastic have a recycling number of 2, 4, or 5. These are usually safe to store polymer clay in.
What about metal or glass containers?
Metal and glass are perfectly safe to store raw polymer clay in. You can use metal boxes or glass jars/containers to store your clay safely without it leeching or ruining the container. Still keep in mind of the lids some glass containers use. Some glass containers use rubber/plastic lids to close it.