For wrapping-paper rolls, a large woven basket works well if you have the floor space. Otherwise, use an under-bed gift-wrap organizer or an over-the-door organizer. If you have a larger collection, a rolling gift-wrapping station can keep paper, ribbon, bags and tools together and roll into a closet when you're finished.
Give incoming items one clear landing spot and schedule a short, regular review so the pile does not become permanent. Keep sensitive papers secure and discard outdated material using an appropriate method.
My final check is practical: can you find what you need quickly, put it back just as easily, and see when the space is getting full? If not, simplify the categories or move the storage closer to where you use it. An organizing system should make life easier, not become another chore.
Mr. Organized's Answer