It all depends on what type of zombies we're talking about. If it's the Night of the Living Dead one-shot-to-the-head type of zombie, I'd go with a Ruger 10/22, a couple thousand rounds of ammo in 30 round mags, a glock 19, a quarterstaff, my CS mini ghurka light khuk, and a tomahawk plus regular camping/survival gear...
You have to remember that in those movies, the zombies had really taken over. There was no hope of resupply, and literally endless zombies seeking to feed on the living. You would want to choose a weapon that allowed you to carry the most ammo possible, which is why I choose the 10/22 and the hottest .22 ammo I can find. My range would be limited, but I would be running for high ground, not looking for zombie trouble. Also, the stopping power of higher calibers is wasted on something that can't feel pain and would not stop even if you blew half its torso off. It's only the destruction of the brain that killed the zombies in the movie, so you only need to get through the head to do the job. Alternately, I'd take some sort of .223 and as much ammo as I could carry with my other gear (probably a couple of hundred rounds)...
I would also be taking the keys to a well stocked 30' Fisher Pilothouse Northeaster Ketch, and not bothering to fight millions of zombies...