I found my pistol before I got the crowbar. The security guard got overwhelmed by zombies and I hauled off with it. Finding ammo for the pistol is really freaking easy, considering that it uses the most plentiful ammo in the game.
For the first part of the game, up until you run into the soldiers, you should be swimming in ammo. Use the crowbar on most enemies, pistol for pesky enemies, 357 for vortiguants, and you usually have a security guard friend with you.