First you need something to pack all of your gear in. It needs to be big enough to get a lot of items in and yet still be portable. A backpack is a good choice. Preferably the type you take on a real mountain hike, but you need to still be able to move around and be nimble enough to escape a large group of voracious zombies.
Now what to put inside the pack. There are a few no brainer items such as food and water. Maybe some protein bars or other small, nutrient rich foods that you can eat on the run. Radio and lots of batteries so you can keep up on what is going on in the world. Some first aid items are also important to pack. You want bandages, antiseptic, elastic bandage, sutures and tape.
Now on to the weapons. What weapons are good against zombie? If you answered none, you have a point but you aren't being very helpful are you. A gun is small enough to pack and will stop a zombie if you hit it in the head. Large knives or cleavers can help if they are sharp enough to take off a head. But then they would probably not be very safe to pack around.
There are a few other necessities you'll want to pack. Be sure to have some flashlights for when the lights go out. Paper and pens to write your memoirs and a Suduko book for those down times.
You'll need to keep your gear in a good spot, preferably a