Magic
There are lots of examples in zombie movies of people who are not Average Joes. Like, everyone with military training, and there tend to be quite a few in Resident Evil. Also, if you allow your players to rest for eight hours uninterupted whenever they like, you aren't really playing a proper zombie game, are you? And I did mention being stingy on material components. If every casting of burning hands takes a handfull of sulphur, and sulphur is in extremely short supply, then it becomes a finite resource. And, maybe a low level adept can heal wounds, but they can't heal poison or disease with spells, which tend to be the more dangerous things in zombie movies... You could also adjust the casting time of spells, to make sure they are only used tactically. So, yeah, the adept can cast cure light wounds, but if it takes them 10 minutes to cast it, then you have to already be sheltered before you can use it. Average is good, but if every character is strictly average, then where is the variety? Every one should have a skill or ability that gives them an edge in a particular situation. Like a blacksmith that can make some implements, the gardener who can help scavenge food, or the nurse who knows how to bind wounds. I mean, if you don't want *any* magic in your zombie game, why not play d20 Modern? The only non-magical weapon in D&D comparable to a guns power would be a heavy crossbow, and they take a full round to load. If your zombies are infectious hordes, melee just won't cut it, so the only real option will be to run, every time. And I could of sworn that there is at least one scene in most zombie movies where a group of them is held off through combat, but you won't be able to have that kind of scene without a spellcaster.