Keep em! Even if they stay in storage for a while..or forever. Spare parts always come in handy!
When I move to MI from KS...I packed around 70 or so models in 4 large boxes. Only had a coule very minor repairs (a couple fuel tanks, a wheel or two, etc had fallen off).
Supplies needed...Boxes (obviously!), extra cardboard, Elmers glue, scissors, foam padding, and styrofoam blocks.
The styrofoam blocks serve as supports for each "story"/layer within the box.
Cut the foam padding to cradle the model, like so...
Use Elmers glue to glue the foam to the bottom of the box. Depending on the size of box you use, you can usually finagle 4-5-6 builds per layer(again, depending on size of models). Glue the styrofoam blocks the to bottom and sides of box (these should only be an inch or two taller than the models on that level). Cut a piece of cardboard to fit snug(so it doesn't slide around)...repeat.
You can see, kinda, in this pic, that I have two layers in this box.