Everyone here is missing the same component, longevity of their supplies. A bit of canned food and some bottled water will get you no where, even if you take hold inside a grocery store you'd need heavy rationing to last even a chunk of time. I'm assuming that these zombies will never die unless personally killed, so you need a solid plan.
I'd need about 20 people at the most for this. I'm setting this right where I live so the locations will follow suit. I will quickly grab a few blunt objects (probably baseball bats and then a large shovel) to make my way out of the house, I will then gather about 20 healthy and capable people to work with me. We will hold up in the Walmart or Target here (they're right next to each other here, so I'll pick whichever one isn't occupied or out of supplies.) We would split up into 2 teams. One will stay back, filling all containers with water (as running water will soon disappear, along with electricity.) The other half will head to Home Depot, and grab tons of gardening supplies and seeds for vegetables. We would also get stuff to fortify the entrances and generators for electricity which will be rationed so that we don't waste it.
Keep in mind that guns are hard to aim in real life, especially in a situation like this, so they're essentially worthless. On the way back we would stop at places that have some weapons that don't require ammo or anything, mainly blunt objects (bats, shovels, and the like) and check the sword shop that's here (it mainly sells replicas, but on the chance that they have authentic swords it's worth a check.) We may not do all of this in one trip, but they're things that need to get done quickly. We would blockade all doors with what we can and continue filling containers with water. Assuming it's the right season we will immediately turn the roof into a garden, this is why we stopped at Home Depot. We need soil and supplies for this. We would plant vegetables and stuff and when they're good we'll keep most of it for the winter. We would probably also check grocery stores around before we hole up for good for any more non-perishable food and to the library to get tons of books. You need something to do when not fighting for your life.
We would ration food (especially if we have more then the 20 max. limit) and just make any adjustments needed. We'd upkeep blockades daily and then probably start making babies. Hopefully someone is in whatever store (Walmart or Target) that we didn't go to and also have a good situation so that we can trade supplies if one is in need and there is a surplus. We might even build a small bridge between the two as a little job for people to keep themselves from going insane (which will happen to some.) After that, we just survive.