I'm enjoying the stick-swinging and knife-flinging so much, I decided to keep posting FMA vids through next week too! It is my humble opinion that this is the best art going right now for proven self-defense in any Post-Apocalyptic scenario; but especially the inevitable Zombiggeddon.
When the law breaks down, you'll be the only law you can count on. And the only law that will matter is the Law of the Jungle -- which is the Law of Tooth and Claw. Stockpile those weapons, your teeth and claws, and know how to use them. Ammunition will get short at some point, so you need to be able to deploy the old stand-bys: knives, swords, axes, and spears.
Everyone of them is devastating against the undead. But you have to be efficient. Train hard.