Rifles come in all shapes and sizes from assault rifles to semiautomatics. A well-made bolt- or lever-action rifle offers a defense against the living dead that is as good if not better than the latest military rifles. The single-shot firing capability helps the user to conserve ammo and make every round count. Many hunting rifles are deisgned for the cilvilian market so they are relativiely easy to clean and operate, something not to overlook during a zombie apocalpyse. Lastily I'd reccomend a hunting rifle just because of the sheer number of cilvian gun stores in America. Finding ammunition for a hunting rifle should be far easier than that of an assualt rifle.
At close-range this weapon reigns supreme. A good twelve-gauge shotgun can literally blow a zombie's head off. However it lacks the long-range power of a rifle due to the disperal patern of the pellets. While the resulting effect may not kill a zombie, it may stop a horde long enough to allow you to escape. Like the rifle, the shotgun can be quite heavy and the ammunition is rather bulky. Keep this in mind for long trips. At the end of the day it's useful to have atleast one in your group.
The handgun is synonymous with America. They're light-weight, concealable, and can be used by virtually anyone. Perfect zombie killing weapon right? Not so fast...Imagine all the emotional stress you'd be under if the dead started risiing. Now try to think of hitting a target as small as a zombie's head. Yes the pistol can a life-saver if suddenly grabbed by a zombie, but I would only use it as a secondary weapon.
Dubbed 'the perfect silent killer' the modern cross bow packs the power and accuracy to take down a zombie. Marksmenship is important, but not more so than the rifle. The crossbow makes a great weapon to have in a group, but reloading takes time and strength. If you were alone and found yourself surrounded by ghouls you should have a trusted secondary.
Hand-to-hand combat should almost always be avoided. It's far easier to run (or walk quickly) than to stand and fight. Most hand weapons fall into one of two catergories: Bludgeons and blades. The advantages of hand held weapons are that they are silent and easy to use. Matchettes and axes are popular hacking devices of the undead. Given the restricting weight of many hand-held weapons I'd personally go with a crowbar. It can be used practically as either a weapon or tool.