I live at home, I still go to high school, but my own stocking up has a 72hr kit, couple hundred rounds of ammo, and lots and lots of water. My room is about 20ft by 12 feet, and I keep all this in my closet. I've also got my BDU's in the closet, and I've got helmets on top of shelves as decoration.
I also have glass bottles on the shelves, and a WW2 japanese ammo can, which I plan on putting ammo in.
These things pretty much pass as decoration, and don't take up much room.
The 5.56 and .40 don't take up much room, I could stick em in a drawer in my room, but my parents said they'd rather keep it in their closet.
So...
Keep food, water, ammo, and some medical/first aid stuff. You can easily keep it in ways or places that don't look like much.