That depends. What do you think of as a zombie? An infected human or an undead human?
Resident Evil or Dead Rising?
Ok, now it's choice time.
1. Primary weapon
2. Secondary weapon
3. Melee weapon
4. Special item.
You can have one of each only. The special item can be anything; but it doesn't have to include food, clothing or anything like that. That's stuff you can scavenge.
1. Pump-action shotgun. These are good because you can start to load it; then if you see a zombie you can just pump and fire; and then continue loading; the problem being a lack of range.
2. Pistol from Halo CE. You know, the one that can take out banshees? You need a long range weapon to go with the shotgun; and what's better than an anti-material scoped pistol?
3. Axetinguisher (Pyro style).
4. Gordon Freeman's HEV suit.
But in seriousness;
1. Pump action shotgun.
2. Some kind of semi-automatic rifle.
3. Crowbar or baseball bat.
4. An incendiary grenade; if I get overpowered I would let the grenade off. Zombies wouldn't be smart enough to get away, would they? At least that would stop me from becoming one of them... hopefully.
A flamethrower is good but it's cumbersome; fire is excellent against zombies as it destroys their flesh; but a flamethrower eats up ammo and is really heavy.
The advantages of being this guy: http://nrk.no/p3/blog/kongkord/files/2007/07/pyro_soldier001.jpg
are that you are protected form zombie bites and what not but you'd run out of ammo too quick.
As for Gordon Freeman, he is totally protected (except for the head) from bites and has a crowbar, which is an excellent weapon against zombies. It's between the crowbar and the baseball bat; the baseball bat is light and makes a satisfying cracking noise when you smash skulls with it; but the crowbar has a smaller surface area so it applies more pressure per inch; and it's versatile.
In the case of Master Chief; nothing is getting through that armour short of a couple of elites. But at the same time, to be Master Chief you need to be 8 foot tall and be biologically enhanced.
I'm gonna go with my choices above. A flamethrower is wasteful; whereas with a shotgun, you can stop loading it at any time and fire. A rifle is good for when you need to defend your castle wall or take out enemies at a long range but a pistol is a good all-purpose weapon. A baseball bat, while lighter than a crowbar, is also less powerful and a crowbar isn't all that heavy. As for the incendiary grenade... well hopefully I would never need that :)