Both cardboard and plastic aren’t good for the environment! There is so much of it everywhere. But in the case of storing valuable items, I’d have to go with plastic. Plastic bins. Plastic bags that seal up. Plastic!
They can keep air and the changing elements out of you stuff when sealed tight. Unlike boxes they can handle water on them. Less likely for critters to get in (no chewing).There are bins of all sizes and colors and shapes. They can stack easily and look nice when organized..
My main message is to NOT have a lot of stuff to store, so then the need for cardboard or plastic wouldn’t be a neccessity. But if you must, plastic bins are the best to hold your items.
In the meantime, continue to edit your homes, offices and garages! The key is to NOT have a lot of stuff that is not being used or is important to save.