Asking a nerd what he'd do in a zombie apocalypse is an interesting paradox, see, most of us have considered the scenario and we think was have a plan. However should the situation come up, the question becomes is our plan implementable? See the problem with raiding Walmart or Sam's club is that's the first place most people are going to look for supplies.
Now, for my plan, assuming I could roll with it.
1. Depending on where I saw most people going would help me decide where I'd hole up. I wouldn't want to be in too big a group, as big groups are easy to spot, and unless they have a rock solid defense point (That dog food plant sounds pretty good actually.) large groups would likely be prone to losing people. To say nothing of the possibilities of poor leadership with too many people. I don't have a specific building in mind, more I'd look for something easy to barricade with a good escape route should things go tits up.
2. My girlfriend and family would be my objective to save. The rest of my friends are either too far away to worry about, or not close enough for me to put my neck out for too far.
3. I imagine I would have to. acquiring a firearm would of course be ideal, but a bit difficult most likely. I think I'd probably stick with crowbar and/or Machete for melee combat. The crowbar having the added benefit of being a useful tool for breaking into buildings, or as a good wedge for a door.
The other part of the question of the Zombie situation is the lack of access to things we take for granted. Power would be working for awhile, but bit by bit power plants would go down with no one left to work with them. If you wanted to have it, you'd need to take back the power plant from any Zed inside and reboot it yourself. Food would become a fairly major issue too, given that there would be a lot of competition for it until the Zed's thinned out the numbers of the other survivors (Which of course leads to entirely different problems)
Then you have to ask, what kind of Zombie virus is it? Is it airborne (You're screwed)? Carried by Vermin? Waterborne? Does it infect if you're bitten? If you're only scratched? Or worse, if you just get zombie blood on you? Or perhaps it only takes effect if you're killed by a zombie? Not sure.
Are the Zombies Fast? Slow? Have they mutated into various interesting forms like the ones in Left 4 Dead? Or are they fairly normal garden variety brainmunching shamblers?
...I...think I may have put way more thought into this than I really ought to.