Fill all the sinks/bathtubs/buckets with water.
Take all food to an upstairs location: neighbor's apartment or 2nd story house.
Also, fuel, matches, flashlights, batteries, radio, blankets, clothes, first aid kit.
Depending on urgency, prepare the staircase(s) to be blocked/destroyed as quickly as possible.
Has anyone read the Zombie Survival Guide?
One fallacy about killing zombies is that a head shot will kill them. Not so. The lower brain functions are near the back of the neck, not in the cranium or forehead. Shooting a zombie between the eyes will not stop it. Shooting/slicing half a zombie's skull off will not stop it. Granted, it won't have eyes or a nose to detect you. But zombies don't use the upper half of the brain. When shooting a zombie, aim for the mouth, which has a better chance of severing the brain stem.