The freeze bowl is the part that trips people up, since it needs to either stay cold or be completely dry before packing, never somewhere in between. Everything else about an ice cream maker is a routine pack.
Pro tip: Label a cooler bag holding the cold freeze bowl so it does not get left behind at the old house among cleaning supplies.
Watch out: Never let a freeze bowl thaw halfway inside a sealed box; the condensation that forms as it warms up can cause mold and ruins the coolant gel's insulation over time.