Let me first say how jealous I am, now here are some thoughts.
1) I'm not an expert in this arena, but my opinion is that plywood would be as good a drywall in sound abatement. Plus it would give you the ability to use it as a base for storage or adding hooks.
2) for such a small space I don't think you need a very bright light to make things visible I would recommend a small LED lantern. I'm sure you can find something that will run on C batteries.
3) As far as storage goes, wooden walls would allow for easy changes to be made such as shelves or cabinets. I would mostly see someone storing food, water, medical items. Also don't forget a way to dispose of waste.
4) for your openings you may want something on each side that you can see through and access your situation. Also something where you can use a weapon if necessary. I would think of something like what bank tellers have where there could be room to pass material back and forth, but also no ability to shoot into the structure. Obviously you would want all openings to be accessible from the inside only. I think an inward opening door makes it where it cannot be barricaded or blocked from the outside, and leave you stuck inside.
Some additional things you may want to do:
Make the structure appear to be something unimportant like a closet, you could Sheetrock the outside and make it look like a utilities closet in your garage. Possibly bricks or wood paneling on the outside.
Think about ventilation, possibly a hand powered fan or filter to force fresh air in.
An in floor safe may be worth installing before placing the structure. something like this
http://www.deansafe.com/ecbinflsawil.html?gclid=CKTvjvDqossCFZSMaQodWW4Pww
