this sounds like the zombie survival guide all over.
The reasons zombies are usually so slow is because their nervous system has basically shut down, as have most bodily functions. This is why you can shoot them repeatedly and they don't say "ouch!" and why you are supposed to shoot them in the head (at least in the Romero series). Most of the body processes have slowed down, thus they are slow and fairly stupid. (For example- zombies can go up stairs, have a hard time going up ladders and almost never climb unless it's atop the bodies of other zombies. Thus the rule- don't go underground, but go up and destroy the staircase behind you).
In fact, "real" or voodoo zombies have more to do with a mix of poisoning and brain damage, and supposedly you killed them by feeding them salt.
But we are talking fiction here.
Couple more points-
A person in armor is basically canned food. Kelvar might help, except it might give you too much sense of protection allowing for a swarm of zombies to get you.
It's the numbers of zombies that matter. Heavy machineguns, even submachine guns, are probably not much use. Better off with a carbine- something with a lot of ammo.
And in 28 Days later the zombies eventually die out- either because of the disease or they just ran out of energy and died out. The 28 Day zombies aren't really zombies. They are not dead people that have been reanimated. If you are killed by a zombie in 28 Days Later you're dead. The trick is the infection- since it's so quick you can be infected before the zombie kills you and once infected, the zombies tend to work out.
So if the 28 Day zombies take over the world, get into a very secure house, ideally somewhere remote, have enough food, make sure the walls are really freaking strong, and you might have a chance of waiting it out.
On the otherhand, in Romero Zombies, a body lose rigor mortis after awhile and before the body is reanimated. THose zombies can last up to 5 years or more. In cold countries this is especially true, as a zombie could, theoretically, freeze during the winter months and thaw out in the summer. One would expect zombies up to 10 years, and considering the rate of infection, probably another 10 years as more people turn into the undead.