Food. Buy what you normally eat that does not require refrigeration. And, don't forget a can opener. Again, a 14 to 30 day supply would be my minimum. . . .
Heat/shelter. Home Depot has some heaters that attach to the 20# LP containers for your BBQ. I would purchase a heater and 1-3 LP tanks. I would also get some 4-6 Mil clear plastic sheeting. This can be used to help insulate the home, close off areas, etc.
Protection. If you are not adverse to owning a weapon, I would recommend a Mossburg 500 12 gauge with an 18 1/2" barrel. These can be purchased at Wal*Mart for about $190. I would add to this some #6 to #8 bird shot and some #1 buck shot. The bird shot will not readily penetrate drywall. Being that you are in an apartment, this would be important. The buck shot is useful outdoors.
A *very* important consideration not mentioned is sanitation. At the very least I'd get the sturdiest five gallon bucket I could find, some strong plastic garbage bags and the seat off of your toilet.
Actually, you can do better than that but this will get you through.