Right now I have everything stored away in containers, but I'm moving shortly (and will finally have my own room again, instead of sharing~!) so I'm hoping to put up a shelf so I can display all my Pinkies. :)
I keep my spare parts in the apparently ever popular compartmentalized plastic storage box.
I store the full pinkys on the travel shelf of my bookcase in the living room. I'll have to take a picture as they are all posed to be looking around our travel items as though it was a museum.
I only have one Pinky and one accessory pack right now, so I just keep the spare parts in the display box on my bookshelf and keep my Pinky on top of my Gamecube. I'm going to get a small beading box for spare parts once I start to buy more though!