The Jesus wrote...
I don't give a shit if I sound like a pussy. The first thing I'd do if there was some kind of zombie invasion, would be to find the best place to set up strategic defensive shelter. I'd definitely wanna go out and fuck up some zombies, but they're already dead. You can't fuck with that kind of enemy unless you can fall back just in case shit goes bad. Your best bet would be to start out with enough supplies to last for about a month, find a secure position, set up a base, gather up more provisions and maybe some allies, fortify your defenses, and when all that's done, then you can consider zombie slaying.
Even though zombies have an strength advantage, they're functioning on a lower level of intelligence which means they're slow, dumb, and clumsy. Unless you're as stupid as a reanimated corpse, maneuvering them into ambushes or diverting their attention should be more than easy.
Can I board up with you then if a zombie apocalypse did happen? I'll bring guns.