Well, it all depends on context and location. For the bit where I am trying to find survivors while simultaneously making my way to an easily defended location that's stocked with tons of useful supplies (Wal-Mart or Sunny's Surplus), I'd use the ever faithful machete and shotgun. Machetes have a good amount of power for use in everything from choppin' zombies to opening new avanues of escape or advancement, and they are light enough to easily wield in one hand. Shotguns have tremendous stopping power as well as damage, which is what is preferable in the situation, since I am only trying to defend myself at close range. I'd wear chain mail (which I do know how to make) under a thick, long coat (most likely a trench coat, since I have one) to defend against potential bites.
However, once at my new fortress (Wal-Mart or Sunny's Surplus), I'd switch to a long range rifle that I could easily use from the roof top for things such as head shots or shooting zombies that look like celebrities when I am bored. Of course, I wouldn't forget to barricade any doors and windows to keep those pesky flesh-eaters out. I'd rig up an easily used ladder or lift system to haul up any knew survivors, and anyone who gets bitten gets an instant bullet in their brain, even if it is me. I am careful, and I fully expect (and anticipate!) the zombie apocalypse to happen soon.