Sunchokes don't last very long once you harvest them, so they are best stored right in the ground, where they will keep all winter under a layer of straw. They're great in soups, or pretty much anything else you would normally use potatoes for.
I got these sunchokes from a co-worker in the spring. I dallied too long to plant them, and they started to go soft and moldy in the plastic bag they were in. I planted them anyway, expecting them to rot. But they sprouted, and then the sprouts sent off side shoots, and soon we had a large "fence" of sunchokes on the west wall of the property. Truly a food for the apocalypse.