Everyone should have a ‘bug out’ kit in case of emergencies. Might be a power outage, earthquake, or zombies.
I have a water proof container of strike-anywhere matches, the container has a lanyard with a clip and had been filled with parafin wax. These are going to remain water proof even if I fall in the water, and the wax can be used to start the fire. This is a basic part of my fishing vest. Then fishing lures, etc. Just grab the fishing vest.
Coffee filters. The paper kind. They can be used to filter water to prevent Giardia. You might be on the run and looking at clear flowing water. But if there are livestock or wild deer around the water will be contaminated, the Giardia is large enough to be filtered out of the water. Boiling is best, but filtered will do.
http://www.aces.edu/dept/extcomm/newspaper/feb1b02.html
.22 caliber weapon of choice. I like my Ruger Mark III target pistol. When I run under a couple thousand rounds I go shopping. The other guns are too heavy to move quickly with and the ammo is heavy.
Whatever dry food you have on hand. If you have nothing like jerky or dried snacks, put some flour, oil and SALT into some traveling containers. With those 3 ingredients you can make a lot of meals. Oh, and grab your most versital cooking pan.
I would take a machete instead of an ax because it’s lighter and you are going to be carrying this stuff wherever you go. But you will take what you have.
Zombies are slow, formerly dead people and everyone should be able to out run them.
Preparing for disaster however is a useful mental exercise.
If you are in a major city you are fucked as soon as the supply trucks quit running, you have maybe 3 days before all supplies are either used or stolen. You are not going to be walking out, nor driving out. At least in hurricanes Katrina and Sandy you knew that eventually the Federal government would show up.
What if you do not have that assurance?
I am not a survivalist, but these things are worth thinking about. A few cases of bottled water, a little portable food, a bug out plan, is worth at least the mental exercise.