I probably would use a very sharp machete. Guns need maintenance and won't be useful once you run out of bullets. I can use a machete to build my camp, and also use it to kill the zombies. Are we not that far off from having a zombie apocalypse?!

A zombie killer.

No weapons. I'm just gonna RUN!!!! =)

Cutting off the telly.

Depends on the area you're in, a bayonet would be a good one, it's a short and tough knife, made for survival and killing, a machete is also good, though it's heavier than a bayonet. But a machete would be useful for cutting wood, etc, though, if you caught a fish, or some sort of animal a machete is going to be difficult to cut it with, while a bayonet would be excellent. So a bayonet would be the most likely choice, you wouldn't need to build a shelter or whatever since every building in the world is now free, you'd need something light, durable, and able to be used for many different purposes.