You have to know your zombie types, not because you treat them any differently -- head shots rule, always keep that in mind -- but the different types will inform how you act when you leave the secret hidden bunker. I've listed research and documentary films that will aid you in your fight against the zombies.
1. Voodoo: The original, the "no problem, mon" zombie was a product of the witch doctor. Using powerful drugs and hypnotic suggestion, a person's will could be stripped away and becoming a tool of the doctor. The drugs were so strong that the zombie could only move slowly with great effort. Theoretically, the condition could be reversed, but it depended on knowing what drugs were used (See: Live and Let Die, 1973).
2. Radiation: Radiation causes two types of zombies. The first was uncovered in the 1968 film Night of the Living Dead, where we see the now-common shuffling, decaying, flesh-eating zombies who have some tool use. We learn how to kill them, and also of importance, that fire disposes of them permanently. A second class of radiation zombies was described in Night of the Comet (1984), and these zombies, while dead and decaying, are still sentient and able to converse, and move more quickly than the shufflers
When the researchers came back to cover the Night of the Living Dead territory again in a 1990 documentary of the same name -- confusing, but hey, that's zombie research for you -- we watched Patricia Tallman disposing of various zombies, finding far enough into their undeadness that they cannot use tools.
The British researched the slow, shuffling stupid zombie in Shaun of the Dead (2004), where we find that a cricket bat is a fine disposal tool, although I still worry about transmission of the zombie effect from splatter.
3. Scientists: Basically, it goes something like this: "Hey Bob, this is one ferocious hamster you've infected with this mutated virus. What say we see what it does to something bigger." Then the infected guard/attack dog bites them, and like the stupid morons they are, they go to a hospital and don't tell anyone what they have. While some are slow, shuffling, stupid and awkward, some are not. More on those in a bit.
Viral zombies are particularly dangerous. Where the zombies have to catch and bite you to infect you, their slow speed makes that relatively easy. But viral zombieism can be spread much more easily.
Scientists also reanimate the dead -- see the excellent Re-Animator (1985) as reference -- giving us even more reasons to make sure that all wearers of white lab coats receive adult supervision at all times.
4. Viral: The viral zombie is most often the fast mover, a very animate, albeit still quite stupid, undead creature. They can move quickly and are strong enough to climb obstacles that would give a parkour enthusiast reason to pause. This speed is also a weakness. Where the shufflers can be killed only by cracking the skull -- thus exposing their brains to oxygen, the one thing that stops its function -- the viral fast-mover can be killed simply by running out of energy -- us -- to eat. Shoot a shuffler through the body, and it keeps going until it rots to nothing. Shoot a viral fast-mover, and it will eventually stop, but not until it has chased you into the next county.
Viral fast-movers can be killed most quickly with headshots, or separating the head from the body. But if you have the means, you can settle for busting them up and leaving the A.O. For more information on this, consult Zombieland (2009) and 28 Days Later (2002).
5. Supernatural: Everyone knows that there is no such thing as a supernatural zombie, as there are no supernatural forces. Let's get real here.