Weapons? I'd bring a metal baseball bat, and a gun. I'm unlikely to effectively wield a heavy axe so I'd settle for a baseball bat. Despite the common belief that a gun will attract attention due the noise, I'd still bring one for long distance purposes. If I was trying to survive a zompocalypse, I wouldn't want to be near a zombie.
For clothes, I'd wear any sturdy jacket and boots. For utilities, besides the obvious backpack, I'd pack food, water, flashlight and a Swiss Army knife.
A vehicle will be necessary as well, because my main priority would be to run away.