I'd like to add, the majority of shot you will find probably won't penetrate the human skull at a range greater than maybe 20 meters, and even if it does, a small BB might not do enough damage to the brain to kill it.
If you go guns, pistols and rifles are MUCH better than shotguns.
The majority of guns you will find are quite loud, and I for one am crap with archery, and wear contact lenses/glasses, contact lenses being in short supply, and glasses being unreliable in tense situations) so most ranged weapon for me have the potential of backfiring.
I instead prefer weapons of the melee sort. My main weapon is a 3.5 foot long half inch thick steel bar, sharpened on one end with a metal lathe (rounded for strength) and a handle on the other made from stamped sheet aluminum wraped and electrically welded to the bar, then covered in ducktape for grip. I have named my weapon "fluffy." This weapon since it is strong can be used as a blunt object for cracking skulls, or since it is pointed, it can be thrusted through the eye-socket and into the brain.
The most effective kill method is to knock a zed-head onto its back, hold it down with one foot on it's chest, and thrust the weapon down into the head through they eye.
The melee weapon you choose all depends on your skill (whether you can use the weapon to a successful effect against a staggering zombie), strength (whether you are actually strong enough to not only hold the weapon, but hit a zombie at least hard enough to do damage), overall stamina (your ability to contunue to use the weapon on zombie after zombie in order to save your one life), the weapon's stamina (you don't want your weapon to fall apart after the first couple hits) and most importantly whether or not you think you are capable of bypassing the skull to preform a killing blow, however, the majority of the time, unless you find something perfect, all you will want is something you can bash a zombie once in the shin with for it to fall down giving you a better chance to get away. The best weapons for this are: baseball bats, crowbars, hunting rifle, at least one ince thick dried out sticks (test it a few times on a tree or something to make sure it won't break), pipes, and sometimes, and you won't want to rely on this, a good old fashon shoe; a swift kick to the side of the leg near the knee, or a hard stomp directly against the knee can have the same effect.
WHATEVER YOU DO, DO NOT use a golf club. They are quite weak and will break very easily.
If you have ANY questions, don't be afraid to reply to this or send me a message. REMEMBER, it's your survival here.
my best answer is to go to your nearest cabela's
reloading suplies, bullet casting supplies, restaurant, knifes, axes, hatchets, camping supplies, fishing everything, cloths, boots, cooking supplies (outside of restaurant), tents,
best bet plan a head. 12 gauge shot gun and rounds of slugs. 1 sulg at 1 oz at 1600 feet per second can drop any living thing on earth ask a hunter. small arm 22 rifle not the same stoping power but better odds at 50 yards than a bat. a string wepon is good if you have any clue to use it. im not talking one summer at camp either you need to be able to hit the head in one shot.
i do feel you always want a solid wepon as well. guns run out of ammo yes but if i drop 100 zombies before i run out thats fine by me. people like swords. good choice if its real. most all people buy are fake. to find out go smack a curb as hard as you can 5 times and let me know.
keep it simple and strong. crow bar is best. its light and you can break in to places if you need. good luck