A semi-automatic weapon would be your best bet, due to the superior range and stopping power to a simple hand gun, and can be used in both single-shot and three-round burst. While fun as all hell, an automatic weapon's purpose is to use a lot of ammo to hit a lot of people, but more adept at injuring than killing. I mean, you can snipe with one, but that's difficult no matter how good you are, and the biggest issue during the ZA is going to be ammo conservation. Problem with a rifle like that, though, is that you'll have to know and practice how to fire one for it's range to be of any use to you. A good handgun will also be good to have for narrow halls and rooms where a larger weapon will be a little difficult to maneuver, but their stopping power (depending on caliber) is questionable at times. Really, range is going to be your best bet. Like I said, you can also switch to a three round burst in case of crowds. While blood loss an organ failure might not stop a zombie, heavy tissue damage to their legs and such will certainly slow them down so you can back up and take a more precise shot, or approach and eliminate with a blunt/sharp object to conserve ammunition. Also, if we're talking about zombies that detect by sight then the knowledge of how to make simple smoke grenades (and a lot of potassium nitrate) will get you far.
If there's one weapon you really want, it'll be a shotgun. The range is horrible, even compared to a pistol, but you'll pretty much stop anything coming at you with a shot so your aim doesn't have to be impressive. End of the day, having a shotgun, pistol, rifle, and a solid ash baseball bat will keep you going. If it's the noise type zombies, then you'll want a weapon that can cave in a skull without alerting everything for hundreds of yards around.
While I'm at it, before any of that, you'll want some kind of fortification to get back to and keep you safe during your down time. No amount of equipment is going to save you while you sleep. Solid doors and bars on windows for one, means of leaving and entering undetected by both zombies and wandering marauders, things like that.