In real life? I'd probably eat a bullet as they started pounding on my door/window. I do a little bit of prepping for an economic breakdown, but I don't think I could handle friggin' zombies.
In a game? Well, you need to decide going in how you want to handle the metagame. The people holding the "idiot ball" are oftentimes just genre blind. It makes for more suspense than watching a group of people who know what's happening and have been preparing for it for years (although that can be fun in its own way, too). Are you going to let your characters be genre savvy? Are you going to ask/trust the players not to metagame? Are you going to change things so that "zombies don't work like that in my game". The last is doable, but it could take some of the fun away not knowing what to expect. Why play a zombie game if it's nothing like how you think of zombies?
I'm in a "Dead Earth" game on another site. It's nothing like the zombie movies I'm used to, but it's been a lot of fun so far.