The most important thing you need is a good hideout:
Even the most dedicated zombie hunter has to have a place to sleep at night where there isn't the constant threat of some rotting corpse having a little midnight snack on your noggin.
You have several choices as far as a hideout goes:
a house complete with boarded up windows and large bars across the doors
a fallout shelter
a shopping mall with all ground level exits blocked. This selection is nice because you probably won't have to do much in the way of stocking - most of it will already be there. Just watch out for looters!
an underground military base
a houseboat
Whichever type of shelter you choose, it should be fully stocked with lots of non-perishable foods, large amounts of bottled water, various weapons with more than enough ammo for them, and some kind of entertainment for you. Multiple exits are also a good thing to look for in a hideout. (You could attract the zombies to one exit with noise and safely sneak out another exit.)
My personal choice would be a houseboat, or other suitable boat. Zombies would not be able to get to you so you could sleep good at night. Having a good night's sleep would make you better able to handle yourself while fighting zombies during the day. A houseboat would also serve as a means of transportation. So if you live somewhere with access to a body of water, find you a houseboat.
**Note: I have been warned that zombies can indeed swim! So a houseboat might not be a very good idea if this is true. Or, it may be that only certain types of zombies can swim. Throw one in the water and find out for yourself! If your zombies can swim, find a body of water with lots of alligators/crocodiles. It is a well known fact that these critters like their food a bit "ripe" - so they are sure to devour zombies!
Vehicles:
There are many choices as far as vehicles go too:
tank or other large impenetrable vehicle, such as a hummer, a semi or a milk truck...
helicopter or small plane (you'll have plenty of time to practice learning how to fly it I'm sure)
a boat to traverse bodies of water (your houseboat comes in handy here)
a motorcycle, specifically a trike (benefits: easier to maneuver than a car; a little more "all terrain" than most cars; and it uses less fuel)
Armor:
What if you are out gathering supplies, get a little careless, and a zombie bites you? You are probably saying "Oh, that would never happen to me. I'm too good." Well, don't flatter yourself - it could happen to anyone. However, if you are wearing some sort of 'armor' that zombies teeth couldn't go through (at least without a little chewing) then you wouldn't be doomed for your little slip up. Your choice of armor, like most of the other items, will just depend on what is available in your area:
BMX plastic reinforced armor
hockey mask or mask used in paintball (a mask could limit your range of sight so be extra careful if you use one)
heavy-duty, steel-toed work boots
leather jacket and leather pants (wear two of each if it doesn't affect your movement too much)
ringmail would be excellent if you could come across any
Other essentials and their uses:
shotgun/shells
blowing off zombies' heads
blowing off your own head if you are trapped and have no other choice
axe / chainsaw
chopping off zombies' heads
chopping them to pieces
getting through locked doors (after all if zombies are out walking around, who's gonna care if you break into a couple of stores?)
flame thrower/fuel
burning stuff, especially zombies
stungun, cattleprod or similar shocking weapon
may or may not work, haven't had a chance to try this one out yet (electricity has been known to destroy zombies before though...)
baseball bat
for backup (you may run out of ammo some time, you know)
shovel with sharpened edge
you can sharpen the edges on a rock if you don't have access to a grinder
nail-gun or power drill
excellent weapon - remember to go for the head
useful in barracading your hideout
hammer, nails, lumber
to fortify your house against the zombie hordes
heavy-duty flashlights
you may need to go out after dark once and a while
it is better to leave your interior lights off at night and use a flashlight instead (it doesn't draw the zombies' attention as much)
fire extinguisher
One of the tried-and-true methods for taking out zombies is fire. It's fun to just light one up and watch it burn. Quite often though the burning zombies will bump about and start little fires. If you are prepared with the fire extinguisher, you can stop these small fires before they do any real damage.
battery-operated radio and/or TV
find out where other survivors are
learn the latest zombie fighting techniques the few remaining scientists have come up with
Note: You can solve lots of potential problems by getting a combination radio/flashlight that runs off batteries, solar power or hand cranks. Click on the picture to see a larger version of the form that you can print and send in.
generator
It is likely that the power will go out once the zombies are running amuck. With a generator, you can still have some of the comforts of the modern world - even if there are zombies running around outside your door :) If you need some help choosing the generator size that's right for you, check out this chart.
first aid kit
One of the most important things to have on hand is a first aid kit of some sort. Everyone's going to be majorly stressed out and is more likely to hurt themselves accidentally. Also, in case of a zombie bite, quick treatment could save your life. Then again, depending on the type of zombie that bit you, you might be better off with a shot to the head. Sad thing is you'll never know until you turn.
extra batteries for all the battery operated stuff
extra fuel for the chainsaw, generator, etc.
...
If you have a museum nearby, you might check it out. You may come away with a little more than culture. Lots of museums have displays of different types of armor and/or weapons used through the ages. No telling what useful stuff you could find there. And who's going to care if you borrow a little bit from a museum - the world's probably never going to be the same again anyway, right? While you are there, just watch out for the mummies though. Take a torch or sledgehammer with you for protection from them. As dry as they are, it doesn't take much to knock them to pieces or catch them on fire!
