Most houseplants only need a quick prep before they travel: secure loose soil, protect the leaves, and control the temperature they ride in. The biggest killer is not the bump of the road, it is hours inside a hot or freezing moving truck.
Pro tip: Snap a photo of each plant's spot in your old home so you remember its light needs when you place it in the new one.
Watch out: A closed moving truck can reach temperatures that kill a plant within a few hours, even on a mild day.