When I store media, I find fungus which leads to rot is one of the main problems so any that will be stored for long, get cleaned fully to remove as much organic as possible than I run them through a light bleach soak like a tablespoon in a ten gallon tank? when done soaking overnight, they will be free of things that might mold or fungus, like snails that might be hidden in the media. then I lay then out to dry fully and turn them to get all of it done. From there, is package them in as airtight as practical for storage.
Carbon? I never use it much but just lay the new back somewhere for times when I might need it for special purposes like to remove meds quick or take out the color from tannins. Carbon is just too much trouble and mess for me to use it any more than that. It's only good for a couple weeks at best so I hate the bother.