This thread is still going?
My only problem with the above is your insistence on a .22 caliber rifle. 5.56 (US military standard) rifle ammo is one of the most plentiful around (assuming you live in the US, Europeans would probably have to rely on surplus 7.62 AK ammo), has better penetration, and is more likely to critically injure the brain, or knock down the target even if you don't get the kill shot. The recoil isn't particularly bad either.
Unless you're Rambo, a bow isn't going to be of much use to you, unless you're hunting for food with it. If the Zombies don't know you're there, why the hell take the risk of alerting them to your presence by attacking them with something that may not kill them on the first shot, is going to take a fair amount of time to load, fire, reload, and fire again, and requires that you maintain a reasonably close range if you really intend on getting that one-hit kill? Sure, it sounds cool, but give me a semi-automatic, high caliber rifle/assault rifle any day.
.22 because it comes in giant bricks, weighs less, does penetrate the skull, is plentiful and so forth. It may or may not go all the way through to skull, but you only need it in to kill. A 5.56, .223, 7.62, etc is fine as well, but you can carry more .22 ammo. The only way to kill a zombie with a gun is to punch a hole in the cranium, and mobility is life, so pick the lightest gun that can still crack some heads. You're also practically guaranteed to find .22 in nearly any house that has a gun.
A .22 is not a toy. A significant number of people die from .22 regarding it a such. The other half of it's lethality, besides people's disrespect, is that it doesn't punch all the way through.
more likely to critically injure the brain
.22 can crack a skull, and even if it doesn't come clean through it will rattle about scrambling brains or ripping rotten tissues. If it penetrates clean through and doesn't damage the brain enough, you've wasted a shot.
200 yards is the maximum range a .22LR should penetrate a skull. That would be the major problem in my list.
A bow is for taking out game, but mostly for taking out people when needed. Noise doesn't matter around zombies so much as is does people. Zombies just sort of have a 6th sense.