Everybody always talks about the weapons they would bring, but what about soap, toothpaste, toothbrushes, cleaning water, and deodorant? They are all important for survival. If you don't use these, your teeth and body will smell terrible and rot about as fast as the average zombie.

Clothes
Also, you will need necessary clothes, bringing into account the season and where you live. If you are in Arizona or Mexico, don't wear heavy clothing. You will develop heat stroke and probably either

1) Get kidnapped and raped, regardless of gender
2) Get eaten by a zombie or 10
3) Die in the hot sun from your stupid mistake

Keeping Clean
If you don't clean yourself, why would anyone want to be near you? Regardless of location, there will be time to bathe (unless you are always running from zombies). Brush your teeth in the morning. Make sure not to use too much water. (If you want to save water use the soaps and shampooes that don't need water)

But take also sure you got some kind of neutral scent on you, smelling too good could probably attract more zombies and smelling too bad would drive away any survivor and potentially team-mate.

Keeping Your Weapon Clean
If you don't clean your weapon, it won't work, and that WILL land you in the most dangerous situation of all, being unarmed. Even the best AK-47 will eventually get dirty, and AK's are the weapons that require the least maintenance.