My collection of banknotes is small, only just over 2000 notes, so it is a little bit easier to manage compared to some of the large collections. I use to work in museums so I store my collection just like I would store artifacts. I use Mylar Sleeves, Archival Containers, and I use Desiccant canisters which I bake every once in a while to refresh.
I originally stored my collection In Archival Boxes in a Fireproof Safe. Boxes are compact and you can store a lot of notes in small space. Boxes make it easy to move things around in the collection. The draw back of a box is that it is hard to view the banknotes. Also, over time the corners break unless you get a good metal edged box. After the fire (my collection was ruined in a fireproof safe, another story), I started to store my collection in Binders. Binders make it easier to view the banknotes. But it is harder to shuffle things around and they take more space.
I now use:
Ultra-pro 3 pocket Mylar sleeves (The2Buds)
Metal Case Desiccant Canisters (Archivalmethods)
2-1/2’Binders with Slip cover cases (Archivalmethods)