Assuming zombies are of the normal kind that slowly shamble around, don't pose much of a threat unless they bite you and go down with significant trauma to the skull, my main weapon would be a .22 rifle (most likely a scoped Ruger 10/22 with box magazine), backed up by a .22 pistol (a 9-shot revolver with medium barrel). I would want a bigger gun just in case I happen across some enhanced mutant zombies or something, or if I have to defend myself against humans (who aren't known to retain their mental sanity when surviving in desperate situations), so probably a 7.62 NATO assault/sniper rifle hybrid. Something compact yet precise, with the option of mounting a scope. Say, a Kel-Tec RFB [http://en.wikipedia.org/wiki/Kel-Tec_RFB], target version (660mm barrel).
Why wouldn't I want a Desert Eagle head-exploder, or giant .50BMG anti-material rifle? Because large calibres and big guns are nice to use in games, but aren't terribly practical, tend to be expensive to operate (ammo is harder to find) and more troublesome to fix (what with having to withstand much higher pressures). There's a reason why no police force is using Desert Eagles.
The lowly 22 Long Rifle round is the most plentiful on the planet, so by using 22 weapons I'd find more ammo I could scavenge, and a 22 is more than enough to penetrate the soft bones of a zombie skull.
7.62 rounds are also plentiful, relatively speaking, so I should have no trouble using the big gun either.
Maybe I'd add a 9mm handgun to the mix, just to be safe. A Glock 17 would do just fine.
Melee weapon... hmm, I don't really know. Chainsaws seem like the ideal weapon to kill zombies with, but they tend to be rather short-ranged and bulky, and zombie blood is not nice to spray on yourself, what with the contagion potential. I'd probably build myself a chainstaff of sorts: the chain mechanism of a saw mounted on a short staff, and ran by a backpack-mounted weedeater engine.
Armor: what Romaru said (basically full-body reinforced armor).
As for the location, I'd try to commandeer a boat or sailplane (provided I had someone who could fly it in my company) as soon as possible, and get myself to a small island. A large ship or oil rig might also work, provided it was zombie-free, or easy to de-zombify with hot lead.
Why? Well, zombies can't swim and aren't known for lasting very long; they'd soon run out of humans to zombify, and then they'd either turn on each other or just die. Either way, in a few months, or possibly just a few weeks, it would probably be safe to go back to the land and mop up the surviving zombies (if any). In in the meantime the vegetation and animals on the island, or the canned food in the ship, would keep me living.
What? No, I don't spend my life thinking of this stuff, it just became all pretty obvious while playing videogames.

I also type very fast and have too much free time.