Let's see...
1) Machete (for the simple reason that blades don't need reloading).
2) Rifle/crossbow - automatic weapons are good against moving human targets, but against hordes of unstoppable corpses whose only vulnerable point is their head? No chance. Even shooting out their kneecaps and then moving in to finish them off would be a bad idea. Better to take them out from a distance. With that in mind, a telescopic sight for the rifle is another essential.
3) Torch.
I'd also get a haircut at the first opportunity - better not to give the undead something to grab onto. Ditto with regard to loose clothing...
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Why so serious?