In a catastrophic zombie outbreak, what you'll quickly find is the most readily available easily-to-use zombie weapon is in the bludgeon category. Bludgeon weapons are any weapons that are designed to inflict blunt force trauma on its intended victim. For instance a baseball bat is the quintessential bludgeon weapon.
The advantages of bludgeon weapons over ranged weapons, such was firearms, or bladed weapons, such as Katanas, swords, and knives, is that they're very easy to use. For my money, I would actually choose a bludgeon weapon; very easy to use, their also very difficult to hurt yourself with. You're not going to shoot your face off with a baseball bat. For the average person who's not a highly-skilled martial artist or not a firearms expert, bludgeon weapons may be the way to go. They can be something as simple as a frying pan. Use this to hit a zombie in the face and get away.
Generally speaking, bludgeon weapons are not as deadly as either firearms or bladed weapons, but they have the advantage of allowing you to strike and get away. Remember, it's not about how zombies you kill; it's about how long you survive. This isn't a video game. Something like a baseball bat can be used as a bludgeon weapon. It can also be used as a distancing tool to get yourself out of a situation. Create distance, get yourself a way.
My primary weapon of choice in a zombie outbreak would be a bludgeon weapon. I would pick a baseball bat, aluminum baseball bat, or a steel pipe, something like that. If you don't have a lot of options, something as simple as a rock can work. Many people suggest using a crowbar and the reason why is that it's heavy, it's sturdy, it's not going to break, it won't bend like a baseball bat might. Another upside of a crowbar that's mentioned is that it has multiple uses. You can use it to pry doors open; you can use it to access buildings.
If we're dealing with the most infectious, deadly, blood borne illness ever, the last thing I want to do after I beat a zombie to death with my crowbar is to then use that for other purposes that may spread that toxic blood around, that days later I might touch, forget about, grab that door handle that I've used the bloody crowbar with, and then touched my eye; 'boom', I'm a zombie.
One of the reasons that I really like a baseball bat is that they're easy to find. They're found in almost every home in the United States. They're extremely easy to use and they don't have a lot of other uses. My baseball bat in a zombie outbreak would only be used as a zombie weapon because I doubt I'll be playing a lot of baseball.