Most of the liteature about zombie events focus on weaponry. The logic is simple: something is trying to kill you-you should kill it first.
That's an excellent way to get yourself killed and to become one of the walking dead yourself.
Weapons aren't what they're cracked up to be. They will give you a false sense of security.
But won't you need to defend yourself against the ravenous dead AND other human survivors who now roam the earth preying upon the weak?
Maybe. Possibly. But it's better off not to put yourself into a situation where you'll need to defend yourself. The smart post-apocalyptic shopper is a quiet, solitary creature.
But it's still a good idea to have a few things to defend yourself.
The best weapon, by far, is also the simplest: the stick.
You can shop for your stick or you can find and shape your own. I hike with a inch and a half diameter stick that's forty-eight inches long that I bought at a National Park center years ago. It's extremely stout, lacquered, and hasn't shown a bit of wear from years of hard use. It also has a leather strap that's well positioned for gripping and hanging onto it.
The Whistle Creek Tracker Series Walking Stick.
I've gripped that stick pretty hard while walking just a few feet from a rather oblivious black bear and was prepared to defend myself and my party with the stout sassafras stick. The better part of valor told me to just leave it alone and be on our way (it completely ignored me). But I was glad I had the stick nonetheless.
You might considering making this your zombie fighting credo: just leave the damn things alone.
A walking stick is a big help when walking long distances, especially when off paved surfaces. It's almost a requirement when walking with a backpack.
A walking stick is likely to always be in your hand and that makes it your first line of defense, and a good one, too.
You can, of course, make your own. Just find a straight, sturdy branch or tree, cut it to length, and strip off the bark.
For advanced zombie survivalists I recommend fashioning advanced stick-based weaponry. Get yourself a sturdy stick about sixty to eighty inches in length and not more than two inches in diameter, then carve one end into a point. Then char the point in your campfire. This will harden it into a very effective spear point. Zombies hate those.