It's obvious you never read the "Zombie Survival Guide"
First off zombies are only dead when you shoot them through the brain and that might even take a couple shots. You can cut off their heads and they can still bite you. Let's say you take an mg, it would be good to "Mow down" the zombies but they will just get back up if they even fall down, which they shouldn't because the bullets will just fly through them and they dont feel pain so they are not going to react to the bullet. You could possibly shoot off a leg though and that would hamper them. The mgs are just too innacurate to hit a large group of zombies in the head with every bullet. You would only draw attention to yourself with one.
The key to fighting zombies is mobility and accuracy. The 3 best weapons would be the SVT, PPSH, or the STG44. If I HAD to choose I'd take the SVT with the STG44 coming in at a close second. The svt combines accuracy and firepower in the same package, so you can shoot zombies in the head with ease and if you need to you can fire fast. The bayonet won't help much except with opening cans of food or prying doors open. The downfall with the SVT is the length, its not real long, but when you are in a hallway it could get you in trouble.
The STG44 would allow for fully auto but you should stick with semi because in full auto you could panic and waste ammo! The stg is accurate and compact enough for close quarter zombie loving. Also the clip holds a good amount of ammo so you wouldn't have to reload as much. The PPSH on semi would be good at medium to close ranges and with the ammo capacity you would almost never run out, however on long shots you are at a disadvantage.
If I had to choose one weapon from WW2, it would be the M1 Carbine, large magazine, accurate, semi auto, reliable, not much kick, and small so you can use in CQC. There now you know how to kick zombie ass and live!