If you can afford to buy nice plastic storage bins, do that. Should keep moisture and vermin in check. I think peppermint oil, mothballs or dryer sheets will keep them away if you want to take extra precautions. I store built models in freezer size ziplock type bags, seal them with a bit of air cushion in them. Place an old shirt or bubble wrap on the bottom of a box and arrange carefully. Use a shallow box ( I use copier paper boxes cut in half an reinforced, theyre super strong, for cardboard) and don't stack built models on top of each other. The next best advice is move your own models, I don't care who's "helping" you move, nobody treats stuff carefully like you would.