I have to agree with the .22LR... to an extent:
As Pulseofthe Maggots said, they are accurate, and the lightweight rounds allow more ammo to be carried.
Also, think about this: if on the move (city or country) you have to eat. You can't carry enough rations to last too long of a while, and would you stake your life on being able to scavenge from stores and homes? The .22LR has been used to bring down game from moose to rat for a very long time (although I would stick to rabbit or cat or something smaller, imagine trying to harvest a moose or even a deer with a .22, though it has been done, and often). Of course, if you're vegetarian that isn't a factor. And I didn't mean to offend anyone with the cat part, but they are made of meat. Don't think I go around killing cats or anything, and eat them, because I don't.
Yet.

Having said that, I think I would want something with more stopping power. After all, its not just zombies you'd have to worry about, but normal human looters and bandits as well.
As for myself, I have to go with my Marlin 336 R.C. .30-30, lever-action.
Light. Slim. Beautiful. My baby...

Plus, a thirty caliber bullet is a man-stopper, most likely an effective zombie-stopper, too.
Now my basic "bug-out" package (I don't aim to bug out, but what else would you call it? besides, you never know) also includes my S&W .41 magnum revolver. They make a lever-action carbine chambered in .41 mag (just like they do for the other big pistol calibers, .357 mag, .44 mag, etc.) but they're hard to find and I imagine they're pretty proud of 'em (i.e. expensive) but that would be sweet, both weapons using one ammo.
