My choices for melee weapons in order of preference, 1 being most preferred to least preferred and the reason why.
1)Battleaxe: one side is a blade with plenty of natural momentum behind it, designed to cleave through flesh and bone and easily caving in the skull and decapitating. The other side is a hardened pick, able to easily punch through most any possible head armor the zombie was wearing prior to changing and the skull all at once. It can be used for mid-ranged melee or brought in for close quarters defense. This was the AK of the medieval era, it can be effectively wielded with little training and can best any melee weapon with enough training, and it's combat versatility can't be matched. Smaller versions, though requiring more force, can be used with a shield.
2)Battle-hammer: you've got a massive amount of momentum to your advantage with no sharp edges (you're not going to decapitate a companion who get's in the kill zone), and still have the pick at the other end you can put even more force behind. For ease of learning, it doesn't get much easier than this, if you can put the sledge end on a slow moving targets head, your almost guaranteed a kill from shear blunt force trauma. For group tactics close proximity to each other, this is the safer weapon to use. Smaller versions, though requiring more force, can be used with a shield.
3)Battle-pick: two pick ends with decent amount of weight behind it, takes more effort to wield effectively in both proficiency and exertion, but almost the perfect weapon for mid-size enemy numbers and not as... messy.
4)Sledge hammer: Though cumbersome, this would be a personal weapon of emergency situations because I use them frequently during my smithing, so I can wield it for longer and more effectively than the average Joe picking it up. Where one would get a few swings in before succumbing to muscle cramps and exhaustion, I can get several in with minimal repercussions and require only brief breaks.
5)Halberd: Though my proficiency with the weapon is lacking, this weapon has all the force of a battleaxe and far more range to it and it can be used as a spear. The extended shaft, though, is more prone to breaking and due to it's range it's versatility is limited. This weapon requires significant training to wield effectively so that knocks it down a few pegs.
6)Spear: This weapon takes a lot of agility and precision to use when it comes to a zombie because all your attacks have to land in relatively small area's on the head, but it can be used to very effectively keep opponents out of arms reach. Smaller versions, though requiring more force, can be used with a shield.
These would be my preferred weapons because unlike quite a few of the next weapons, the most basic skills to be employed are fairly easy to obtain for zombie eradication. The problem is that the zombie eradication skills don't translate in the less preferred weapons because of the narrow training window you have. 5&6 are relatively quick to learn and master for the sole purpose of zombie eradication, but it takes a very long time to branch out to their full combat potential. The following are not as ideally suited for zombie combat, and included will be reasons why.
7)Hand-and-a-half double edged sword: It can be useful with a buckler, but the problem with any sword the ability to incapacitate a zombie. You have to realize that the point any sword is to either slash, stab, or something between through soft tissue. The Hollywood sword cleaving through bone in one blow is crap, to be able to takes a great deal of force and a very thick blade, even then you may not sever all the way through the bone. To decapitate, it could take several blows, especially against a moving target and having to go through so much tissue (assuming a neck blow) to get to the spine. There is a very good reason the axe, then later the guillotine, replaced the sword for decapitation, and they were cutting at the back of the neck which is the ideal place for decapitation. You're most likely not going to get this chance against the undead. However, with an inherently larger cross-section and broader tip (generally), you have the ideal proportions for cleaving through bone. Sharper angles, like those commonly seen in the tips of single edged blades, are prone to absorbing harmonic vibrations. Harmonic vibrations are present when impacting hard objects, and these can cause stress fractures that can lead to causing the blade to fail. The most common area's for this are at the tip and the tang/ricasso area. Tip damage, depending on the fracture, can render the entire end of the blade useless and can ruin the integrity of the entire blade. The tang area is the real danger zone, because if it's not properly heat treated and/or has too sharp a recess into the hilt, it will shear off across the tang. Even proper heat treatment and proper design this is still a danger. Furthermore, the sword requires more effort to get the same results, a killing blow to a zombie.
8)Folded steel single edged H&1/2 sword (katana style): I had a real hard time deciding whether this would go in 7th or 8th. It's 8th because although it's a folded steel(damascus) blade which greatly increases it's durability, you only have one edge. This really increases the skill required to maneuver the blade for consistency, years of practice is required to reach the precision and endurance needed to wield the blade, and to cleave through bone requires two hands due to its weight.
9)Single alloy, single edged H&1/2 sword: All the drawbacks of 8 without the durability.
10)Scimitar style(large curve) blades: These are designed to give you the greatest slicing ability, eviscerating and deep painful cuts followed by elaborate killing blows. Virtually useless for zombie attack other than for defensive purposes.
To build on the reasoning in 7, with any one handed or hand and a half blade, the ability to cleave/decapitate is going to require two hands and a lot of exertion and precision because the weight distribution in the sword doesn't allow for a great deal of momentum. The lighter the weapon, the more exertion you have to put into a blow to achieve a killing blow. Remember zombies do not feel pain so blows designed to inflict incapacitating effects are useless, so your blows have to be kill based or carry enough force to literally push your opponent away to get a killing blow in. You notice I've left out many blade styles and weapons aforementioned that you might consider, but remember that the larger the blade, the larger area you have to be in to use the blade, and you're a greater danger to anyone around you without extensive training. The Claymore, or properly the clamour (great outcry) as it's properly said because of the fear it induced on the battlefield, requires the wielder to wade into battle basically by himself, and armor is limited because of just how heavy the weapon is and the agility you need to cover yourself on all sides. Against an enemy that has no fear, you'd basically have to spin around over and over again to defend yourself properly, hoping your getting killing blows. I like the clamour, but it's a weapon of fear and has no place in a zombie fight. The next weapons require the zombies to get really close and personal, so skill and agility are going to be paramount to your survival with these weapons.
11)Cross-peen or blacksmith's hammer/double sledge one handed hammer: This would be preferred because I use it for hours in the shop, and it is possible to get consistent killing blows in one to maybe two hits.
12)Clawed hammer: Less momentum than 11, but it has a clawed edge that can penetrate the skull so you don't have to have quite as much force, but it's more likely to get stuck as well.
13)Combat spade: A spade designed to be used as a chopping weapon and a thrown weapon. It takes a lot of skill to throw it and get a killing blow, and takes a hefty amount of force to get a killing blow, but it's kinda like the light weight version of an ax, so it ranks higher due to it's utility.
14)Trench spike: Hard to come by, low momentum, the only things this has for it is that the spike is hardened and is designed to punch through helmets and the skull plates, so you only have to supply the appropriate force. The knuckle duster also is a plus since it can be used to force your opponents back without having to touch them, reducing contamination risk, and if you have boxing experience, these can be far more beneficial to you than the aforementioned very close quarters weapons.
15)Crowbar/pry-bar: Aside from popular support, the crowbar is a utility piece that can be used in the zombie emergency because of it's sharpened end(s). What it then amounts to is basically a heavy version of a billy-club or an extremely short spear. It's utility is useful, but it's combat effectiveness is very slim against the undead.
16)Combat knife: These are designed for utility as well as combat, so it makes the list but at the very end. This is because you are going to have to literally ram the knife through the skull, relying almost solely with the force you exert and you have to be extremely close to your opponent and have little guard against contamination other than the protection you are wearing. It is very durable however, and can be used for far more than just combat.
This is my list. Remember this is for killing a zombie, and the only effective way to remove a zombie threat is to destroy the brain and/or sever the brain from the rest of the body. Anything that is designated "utility" or kitchen cutlery or what have you is NOT designed for consistent use severing bone and/or punching through the skull without extreme maintenance procedures, and even at that they will still have a very limited useful life.
Feel free to critique and list your own!
Dare you not mettle
in the affairs of dragons...
for you are crunchy and taste like chicken...
and come prepackaged with ketchup.