Don’t underestimate the value of simple traps. Nail boards and caltrops can wipe out hordes of melee oriented creatures with minimal risk to oneself, and do not have to be reset when activated. Adding a smooth surface and roller blades or skates, and you can literally dance around zombies and not once put yourself at risk as the traps thin out the ranks.
This technique can be used as early as day one, and can clear out a school, mega store, hospital, mall, etc. in the manner of a day or two provided that one remains vigilant in regards to ranged threats. In addition, there is no morale penalty for killing zombie children in this manner.