Reading this thread has me concerned...
I'm afraid too many of you are thinking of how you would address a conventional attack - by that, I mean an attack by the living. People are throwing around terms like "stopping power" and I've even read a suggestion about a flame thrower... PLEASE

!
These walking killing machines laugh at this conventional thinking... or they would, if they were capable of understanding humor.
A Zombie has no fear, and more to the point - no feelings. That means burning them (ala flamethrower) is a double edged sword. While the flames will eventually consume the Zombie corpse, you will still have up to an hour with a bumbling, slow moving, WALKING-lighter, bumping into anyone and anything (INCLUDING YOUR SHELTER!!!) Unless you plan on smoking yourself out, lighting a Zombie up should be done with the utmost care!
Now, when it comes to handguns... forget "stopping power." If you shoot a Zombie in its arm, or its leg, or even its chest, it will STILL KEEP COMING! All you will have done is wast ammo and possibly drawn the attention of other Zombies in the area with the noise of your weapon! You want to look for 2 things in a handgun when it comes to Zombie defense - 1) Ease of use (including under harsh conditions - you may be on the run) & 2) a large ammo capacity.
All you need to do is scramble the eggs between their ears... so a 9mm will be fine. The ammo is plentiful and light compared to other calibers which means you can carry more! If you know you will be traveling through especially harsh conditions (i.e. swamplands and such) then you may want a simpler firing mechanism such as a 38 revolver. Just be sure to shop for your anticipated environment!
Lets talk rifles...
The two best options are... wait for it-
The M1 Garand
The M1 Carbine

With accuracy, light ammo (the advantage of which is described above), and a quick rate of fire - these two babies are all that you need.
Remember folks... it's all about the head-shot. If you pull out a spray and pray weapon, well lets just say you'd be better off by dropping the spray part.
The ultimate shooting weapon when it comes to the Zombie appocolypse?
Simple

Think about it... it provides you with distance from your grabby foe, accuracy for the killer headshot, and best of all -SILENCE- so you won't grab the attention of any more of the undead in the area...
The two best close combat weapons would have to be the Army surplus machete, or a crowbar. The Army surplus machete for the obvious reason that it provides reach with an effective kill stroke. AND because the blade is usually painted black- perfect for those full moon nights - you don't want anything flashing out there.
The crowbar is good because of its versatility, both as a weapon and a tool. You never know when you'll need to jimmy a door to make your escape.
Folks... i'll stop here-
Do yourselves a favor and go buy
Read it... take notes... make your shopping lists...
The threat is real people... Organize before they rise!
