Personally I prefer a classic wooden coin cabinet for my copper and bronze proofs. I've got several cabinets, and this is the quite small one I use for my proofs. Walnut, with untreated mahogany trays so as to prevent leeching/contamination. Untreated mahogany is always the best wood for storage.
Incidentally, talking of copper proofs, I wouldn't be at all surprised to see quite a few in Noonans auction of the Philip Richardson collection of George III coins on 3rd October 2023 at 14h BST.