I manage a storage facility with a Uhaul dealership.
Packing tips? Try to use uniformly sized boxes. Use SMALL boxes, not mediums. Fabric is heavy, and someone has to lift those boxes once they're packed. Someone else suggested using fabric to pack around breakables. Good idea.
I ALWAYS recommend when you rent a Uhaul that you get the Save Move damage waiver (insurance)!! Considering that Uhaul thinks those trucks/trailers are made of gold under that orange and white paint, and that they don't deal with private insurance companies, most of which do NOT cover Uhauls anyway, you get to pay out of your own pocket for any new damage, regardless of fault. Then you get to deal with your insurance company to try to recoup all or part of your money...it can take months!
If your fabric is going to be in a storage unit, put out the money and buy some Decon (mouse poison) and spray the unit before you load it with bug spray. Most storage places try to control pests, but we try to control them in our homes as well, and don't always succeed....nothing worse than opening a box of fabric (or anything else) and finding a mouse nest, or holes in stuff!!