Most of the Zombie novels I've read don't specify how they started. My advice is go with the cure (insert favorite disease here) goes bad and run with it, or a biological weapon accident. I would stay away from a nuclear bomb, too much damage, and you always have to deal with the effect radiation has on your story line. Your reader will expect something on how radiation is affecting things. On the wasteland Zombie hunting team, have a group of solders or police meet up with a group if civilian archers. If you think about it bows and arrows would be the prefect Zombie hunting tool. The downside is rate of fire, and they're very hard to master. You will have to factor in your story line how the archers got thier skill, maybe a college/high school archer team.