I would sell what you can not take at a small discount to a family that is also into stocking up.Better than giving it away free. I know I would buy it!
Best thing to prep when moving often is: take your knowledge of gardening, and seeds. When you get to a new place, scrounge any kind of pot you can pick up at yard sales. Move some grown lights; buy new bulbs to lighten your load. You can get a couple years of good hearty FRESH produce, then when you have to move, sell the potted plants and the light bulbs, but move your grow light fixtures and seeds.
Remember that there are also seeds can also be sprouted for fresh microgreens and sprouts.
Instead of canning or saving your dehydrated produce in jars, use the seal-a-meal-type products which will also lighten the loads. Use rags instead of toilet paper and paper towels.