Either or doesn't really matter. I keep all of mine hung up in my closet. you might want to soak them in very mild detergent first then rinse let dry then store. I do my booties and gloves too since they tend to smell like...well you know that smell
I've been hanging mine for years without problems. Just make sure you use a hanger with wide shoulders so no one point has a lot of pressure. I've laid some out in the past and when I took them out of storage they had a permenant crease along the side. Now I hang all of them.
For those on a budget from what i've heard, wetsuit shampoo = woolite. Either way, i've washed my wetsuits in warm water plus woolite for years without any probs and they come out of storage smelling fine. As for hangers, plastic and wide.
Hang your suit at the waist, "inside" the hanger, or folded in half, to prevent any problems with the hanger poking into the shoulders.
I would think that you would get a permenant crease along the fold this way. Hanging by the shoulders on a wide hanger is probably the better option. You can buy suit jacket hangers at most supermarkets.