Starting a campaign from the middle-part of the zombie apocalypse. Some ideas I had:
Have the players form a gang/survivor group of their own. Each character will have a backstory about where they began and their trigger event for realizing something is going down the toilet in the world.
They will have a limited armory at the start of game (I will be using Hero for this, so I can use character points to "balance" starting equipment) where they get to choose their weapons.
They will have a definite purpose at the start of the game, probably having to relocate (a horde is coming) or find parts for a generator. Whatever it is, it makes an adventure necessary :)
Include whatever flavor of horror/mystery into the game world, and have the player characters run into hints of it during play (ex. a different kind of zombie) and have them decide what to do about these clues.
Counting bullets, bandages, medicine, food, water, gasoline all of it should be sparse and requiring constant expeditions to keep the camp supplied. If the characters are on the road, make it always possible to gain what they want but put it behind challenges they are required to overcome. Miniatures battles/stealth missions start when these expeditions run into problems.