I would use a assault rife and something to break the lower half of there jaw off because even if I could kill the zombie at the moment, at least it wouldn't infect anyone else.

A nice big steal sword, followed by a Uzi, a hand gun, and a shot gun.

I would carry around a variety of weapons. I would have some melee weapons such as a crow bar, or baseball bat for up close and personal fighting. Then for long range or mobs of zombies I would use firearms such a shotgun for the mobs. However I would use my guns sparingly because I wouldn't know when I would find more ammunition.

First, the only thing that would happen when killing zombies would be getting bit.  My strategy was be evasion and hiding.  Why kill them?  That's bad news.

I would select quiet weapons that don't need to reload.  A crowbar would be used as a weapon and also as a tool if I needed it.  Same goes for an axe.  They'd be dual-purpose, silent, and would never run out of ammunition.

I don't own a gun. 

To be a bit more realistic, I would hide. I would stock up on some quick supplies, and find a good hiding spot. 

If I have to get a weapon, I would take the kitchen knife set, a broom, and whatever else that I have that may be useful for anything,  not just for killing zombies.

Honestly I'm a little off so I would have three shirts a sword and a sniper rile. One being worn normally, one being worn as a ninja hood and the third would be for the ones that catch me off guard and get close as a defensive kind of ordeal. The sword is obvious though id make sure to have a sharpining stone so when it started dulling out, I could cover my tail there. The sniper for covering survivors from other neighborhoods. 

I expect the conversation is about weapons we could realistically get our hands on and employ.  I don't know if you folks know how to use flamethrowers, machine guns, and the like.

Me?  I'd go with something that never reloads and would be useful in multiple situations.  An axe is good because it can break into buildings and kill zombies and humans alike.  A crowbar would smash a head in and destroy the brain and could be used to pry into buildings and facilities.

Generally, going after and fighting zombies would be last on my list.  I'd be digging in, hiding, waiting, and make quick forays into other areas for survival supplies like food, water, and the bare necessities.  I'm not looking for any zombies until things blow over.  I'd stay away from guns and firearms.  They're nothing but noisy ways of attracting zombies.  Guns are tough to use in long range and I'd steer clear so someone doesn't get killed accidentally and i didn't attract unwanted attention.

Double barrel shotgun with buckshot shells, machete, sledgehammer. If it's good enough for Dawn Of The Dead, it's good enough for me.

Sword that is light and easy to use, like machete or katana.
Pistol with suppressor so other zombies/people can't hear you when you kill a zombie or human.
Maybe a sniper too, if you have some kind of fortress you need to protect, and of course some mines and grenades.

I would use a cross-bow, rifle, and a sword. 

The cross bow would allow for quick, lethal kills of zombies that are several yards away. It's really helpful when picking off a few when a hore is rushing and killing those who get too close. The arrows can be used but they can be left behind if there's no time.

The sword would be good for keeping zombies away in close range and trying to slice off their heads. My only worry would be getting it stuck in a zombie's body. 

The rifle would allow for a few long distance kills or detonations, whether as a distraction or mass-killing zombies.

I would grab a Pitchfork and take off the trident end and then attach a sharp, long stake on the end, like a bayonet. Or I would pick something more ealistic, like a pitchfork with an underslung shotgun.