What I did when I was in an apartment with friends was I wore only at night, or when they were not in the house.
If I wet them, I would put them in a small plastic bag and would always take the garbage to the dump. If you are worried about them hearing when you put the diaper on, you could always put on some music on a speaker or turn on a radio to drown out the sounds.
As for storing them, under the bed is an option, back by the wall. or if the place has a closet, you could put them there. I have also stored my diapers under drawers where the entire thing has to be removed before they can be seen.