Knowing the history of the zombie concept is essential. They first entered popular culture in 1945 in an article by Dr. Louis Mars. After that George A. Romero is credited with producing the bulk of zombie culture in the U.S. through his many films. Make sure to read up on the folklore and watch the films of Romero such as "Night of the Living Dead." There are also multiple comic books and novels available, such as Max Brooks' "World War Z," for reference.
Is an apocalypse necessary? Not really, but it's highly encouraged. If there isn't a massive extermination of humanity you'll have to explain how the zombies exist among the living. The film "Sean of the Dead" has an ending that seems to suggest this type of coexistence, so it's not unheard of. The apocalypse angle is advisable though from a plot and fandom point of view. Zombie fans love to talk about the zombie apocalypse, and they'll love to see how your characters survive it.
Zombies come in all flavors: smart, stupid, fast, slow, etc. Some retain memories, some don't. These are all decisions you will have to make when writing. However, you should know there is a type of zombie fans hate: the un-killable zombie. Your zombie can be fast and stupid or slow and smart, but he can't be fast and smart. In short, he can't be better than the humans. If the humans don't have a chance for survival your audience will have nobody to empathize with and will lose interest quickly.
What makes your book different from the other zombie books out there? After doing some research in the current market, you should be able to figure out what differentiates your work. For example, "World War Z" can be said to be social commentary as well as entertainment. In order to discern how your work is different ask yourself some questions. What kind of effect do you want to have on your readers? Do you want them to laugh? cry? cringe? What audience are you looking to appeal to? Romero nerds? Mainstream America? In other words,what is your book going to do that other books don't do?