You'll now be in a short corridor. As you approach the end, a cinematic will trigger, revealing your first zombie. This is a scripted event. You can try to fight it, but it's often best to conserve ammo at this stage. If you're playing as Jill, Barry will intervene and save you. If you're Chris, you'll have to deal with it yourself or run.
After the encounter (or escape), proceed through the door at the end of the corridor. This leads to the West Wing Corridor. Immediately to your right, you'll find a door leading to the Save Room. This is a safe haven. Inside, you'll find a Typewriter (for saving), an Item Box (for storing items), and some Handgun Ammo. Save your game and deposit any unnecessary items. You'll want to keep your inventory as clear as possible.