I moved my collection across country twice, not to mention shipped many to people I had built for including large sailing ships. I prefer the styrofoam block method. I suspend the plane off the styrofoam with toothpicks or wooden dowels. then I strap the model onto the styrofoam block with monofiliment line by poking holes into the block and wrapping the line around it. I have also used strapping tape with paper over the model so the tape doesn't stick to the model.
I then place the entire assembly in a rubbermaid container and fill it with cotton that is used for stuffing teddybears. I also have used florist blocks, those green blocks that they use for bouques, and cut out an outlins of the model, say a ship hull or car, and place it in the block, cover it with cotton, and put it in the container.
Anther container that works well is accounting file boxes. These come in a wide array of sizes, stack well in a van or storage unit, have a top that lifts off and ties shut, are strong double ply, and have handles.
The problem I had with using peanuts or paper was when a part fell off, it was next to impossible to find it without a lot of sifting and then having to clean up the mess. With cotton, the part will stick to the cotton and stay in the proximity of where it fell off at.
Good Luck
Scott