I don't own a gun or any serious medical supplies. If I could only grab what I had in the house, I would take a 2/3 scale crowbar, a carpenter's hammer, a large kitchen knife, and the keys to my car. Also I would put on my leather jacket and work gloves to help against bites, plus an eye guard like you wear in wood shop. Assuming I beat the zombies immediately outside before they broke in and devoured me, I would come back for canned food, spare clothes, a maglight, and a backpack.
If you're offering me my choice of weapons, I would basically Left 4 Dead it: a really solid deer rifle, a semi-auto shotgun, a large caliber automatic handgun, and either a bigger crowbar or a fire axe. Add heavy work boots, double-thick workman's jeans, night vision goggles, a helmet or hardhat, headband flashlight, knee pads. Vehicle of choice is an armored van with runflat tires. Fill that sucker up with food, bandages, extra set of clothes, spare gas with siphon, spare tires with jack and lug wrench, ammo, spray paint for messaging, telescoping ladder for quick rooftop access, and gun cleaning kit. Off I go.
I live in a rural area so I wouldn't have to worry about hordes stretching to the horizon. Packs of fifty or less is the most I'd see, and that only in the center of town (still a problem, of course!) My goal would be to drive north to an even less populated area, or barricade myself in the office of the local Home Depot, which is right next to a supermarket. Every day kill a few more until there are none. The parking lot would offer a really good view of approaching zombies. I could park in the middle, climb on the roof, and plug away.
Video games notwithstanding, anything that causes fire or explodes is just too dangerous, so I would eschew molotovs, grenades, etc. Zombies don't feel fear, or pain, nor do they stop to pat themselves out. Even if you set them on fire, you're still being attacked, they're still every bit as mindlessly aggressive, it's just now they burn you as well. It takes a long time for the body to burn so badly there's no motility left.
Edit: (rereads initial question) Okay, now I feel silly. One weapon....gotta go with autoshottie. My hammer if I'm limited to what I have in the house.