I can't tell you which is the most optimal method, but when my collection was put into 9 months storage and - after that - shipped across the pond, this is what I did:
I had a pile of acid-free tissue paper lying around, so wrapped each object in a cut piece (letter/A4 size). Placed the wrapped objects in cardboard boxes (a little bigger than shoeboxes) and finally placed some bubble-wrap on the top to keep stuff in place before closing the lid. Then taped the lid to the box to keep it closed (and to indicate if it had been tampered with).
Obviously that wouldn't stop things from moving around inside if someone shook a box violently, but for normal handling I assumed it would be fine. And even if stuff moved around inside, the objects would still be wrapped individually and not hit each other directly.