For close range the ideal weapon would obviously be a chainsaw. But then you would have to worry about fuel, so it might be a good idea to keep a katana strapped to your back.
Chainsaws are bad ideas. They can run out of gas, they can jam up (especially when covered with blood), they get dangerous to the user (especially when they're slippery with blood -- see Dawn of the Dead 2k4 for more info), and they're really noisy, which attracts more zombies. Other than looking cool, there is absolutely no benefit to using a chainsaw on zombies.
A katana, kept sharp enough to cut through a neck, would work well. Failing that, a club.