Depends on the type of costume and if you want the helmet inside it or seperate. I have a bunch of different kinds of costumes and almost all of them are in the generic Walmart box Jim has posed on the top here. They are completely awesome for transport and storage, I love them!
I can fit in them: full Biker w/ helmet, full Tie Pilot w/ helmet, custom Mando w/ helmet (small backpack, no rocket or backplate though), Jedi General (w/ armor), regular Jedi, Admiral Veers, X-Wing pilot, and a few more.
I have some larger, like 30-35 gallon rubbermaid bins for my Snow Scout, Snowtrooper, Commander Neyo and upcoming Animated Clone. They could fit in the Walmart bin but not with the helmet, and I like to have the buckets with the costume. Snow Scout and Snowtrooper have the large backpack with eats up the space, the Neyo has a lot of parts and I could fit the TK in a smaller bin but I have a lot of extra stuff with that costume.
I have one of those sweek Home Depot rolling ones, it's HUGE and works great when I go to a troop and want to put more then one costume in it - I'll throw in mine, my son's and wife's all together and then we need only roll that one bin instead of carrying them all seperately or stacking them on a handtruck, but it's waaaaay bigger then you'd need if you wanted to simply put one costume in it, at least IMO