You know, it's a little different when it happens 200 miles away and when it happens less than 20 miles away... what caliber for zombies again?
It doesn't matter, as long as you can make head-shots with it. .22LR should be adequate, but I hate to trust rimfire ammo. (if you do, CCI MiniMags seem to be the best that's reasonably priced) Do you have a .30 Carbine, or .223, or an AK or SKS?
Good old .30-30 is a good one if you can carry enuf ammo and reload in a hurry.
Until I got a Mini-14, my zombie gun was a Marlin 1894C loaded with .357 Magnum lead wadcutters (full-power, not target loads)
I'm taking this question way too seriously, aren't I?