I would make the zombies completely un-turnable. The concept of turning undead is based on exorcism and vampire legends, not on zombies. In fiction, zombies are completely unaffected by a strongly presented holy symbol. If this is the basis for an entire campaign, then I would give clerics an extra feat or domain to make up for the inability to turn undead.
Some posters have mentioned using ghouls instead, but I would start out with normal zombies, and then work up to ghouls and greater undead. In several zombie settings, the initial undead are pretty much mindless zombies. But then, after a period of time, they begin to become more intelligent and organized. They start displaying personalities and intelligence and even additional abilities. If you do this, the PC's really experience the horror aspect of the setting, because as soon as they learn how to deal with the threat, it mutates into a more dangerous form. I owuld imagine the PC's would survive the inital zombie horde, perhaps realizing that the movement limitations of the zombies means that the PC's can always outrun them if they need to. Then they would be truly horrified the first time they see one of the zombies break from the slow shambling pack and just start running full speed at them.
I would also be sure to consider the extent of the zombie infection, how it spreads, and the means, if any, to end it. In "The Rising", the author allowed the zombie plague to affect all animal and insect life, and anything that died would come back, regardless of getting bitten, and there was no way to stop or reverse the plague. Plus, the fact that all of the animals and insects were affected meant that even if somehow the plague were stopped, the ecology of the entire planet was already destroyed. That made the initial threat perhaps more interesting, but ultimately made the story pointless (IMO), because the heroes had zero chance for an eventual victory or escape, and part of the tension in a good zombie story is that the heroes just might make it if they can just hold out a little longer. (In Night of the Living Dead, they just needed to survive until help arrived. In 28 Days, they just needed to survive until the zombies starved themselves out. ) That slight chance of escape or victory is what keeps the tension from turning into despair, at which point it gets boring.
Also, a large portion of the shock of a zombie film is in seeing the harmless and familiar become dangerous and alien. Specifically, seeing empty city streets and burned out buildings, seeing the PC's home town become a battlefield, seeing the beloved NPC's turned into monsters. So just dropping them in during the first session with a bunch of zombies, they will miss out on that. I would recommend at least a few sessions or an entire adventure to give them time to get comfortable before unveiling the undead. Maybe have hints and rumors in the first adventure of a disturbance in the next town that the PC's ought to check into as soon as they are done here, etc.
Finally, I would be sure to have some goal in mind for the campaign, either for the PC's to escape to an ultimately zombie-free area, or for them to somehow eliminate the cause of the plague, and try to plan out how they will get the information that they need to make that happen.
