It's always good to have a list of what you should be hunting for when looting houses and such, if the apocoplayse surfaces and whipes the Earth away, and you were lucky, then have this list close on hand.
Flashlight - Flashlight is obvious, it helps see in the darkest places, keeping you from finding any zombies or falling down that hole. It's also good to see what's making that weird noise.
Batteries - Batteries are for everything, for your flashlight, your phone, your radio, and your clock. They are a must when you have things like Flashlights.
Water Bottles - You need to drink water, which is the most important thing in surviving the apocolaypse
Water Purifier - If you run out of water and you need to use pond water, you have a water purifier so you can drink it. Dying to a disease is the worst way to die in a n apocolaypze
Food - Canned food is your best bet, but when it's the beginning of the apocolaypse, you can find basic things, such as cold things, but they won't last. So canned foods should be your focus.
Silverware and Plates/Mess Kit - Things such as silverware and plates are more important then you may think, imagine it this way. Your eating something with your hands and the precious food falls from your hands, making it dirty and uneatable.
Lighter or Matches - If you don't have a flashlight, these are a good bets, plus they make it easier to start a fire.
Soap - This isn't a major thing but nice to have, a soap to wash your hands or body.
Sunscreen - Sunscreen is very important when traveling by foot or just being outside for too long.
Hat - Hat has the same job as sunscreen, it helps shield your vision from the sun though, which can help when watching for the walking dead or people.
First Aid Kit - I cannot stress the importance of this. It could be a small one with basic medical supplies, but they'll help when you get a cut, slash, or any type of wound, having some disinfect and bandages will do a lot, compared to just water and a dirty rag. Dying of a infected cut from a rock would be a way to die.
Duct Tape - Duct Tape can help a lot, from fixing a car hose, to setting up traps, patching things up and fixing the comparment on things that require batteries that keep coming undone or even shutting the mouth of that one talkative guy that is going to get you all killed.
Binoculars - Binoculars are great for scouting around, watching for people and zombies, looking for help and searching for anywhere to loot.
Tent - If you have to camp out, if you cannot find shelter, this is your best friend, it's safer then sitting out beneath the stars and gives you a bit of a protection from the elements.
Sleeping Bag - Sleeping bags help keep you warm, but prevent instant movement if something attacks during the night.
Blanket - Blanket is better then sleeping bags in some ways, it may not warm you up as much but it allows free movement.
Goggles - When slashing through things, it may be better to protect your oh, so sensitive eyes which could get the infected meat in them, and turn you.
Gas Mask - They are useful for if the virus is airborne, or if a zombie wants to give you a kiss and if none of that is true, the smell of dead bodies will make it worth it.
Compass - They are great for survival in general, they show you if your heading the right way, what way to go if you need shelter and to make sure you aren't going in circles.
Gloves -
Gloves are handy because you can lift, or move bodies without worry of getting it on your hands, or if you need to fight off infected with your hands only, it's better then having bare hands.
Backpack - To carry all the items above, especially useful when traveling on foot, I would suggest a hiking backpack though
Melee Weapons - Great because when you run out of bullets but you have to get up close to use it. Also good for using when in need of quiet weapons
Crowbar - Crowbars are a good melee weapon as well as used for opening things plus they aren't to hard to find
Guns -
Guns are needed when fighting the dead and the living, problems...? Running out of bullets
Bullets - You need these for guns... And lots of them
Vehicle - Any type will do but bicycles, motorcycles and jeeps are not suggested as you can be pulled out. Don't worry too much about gas, so many abandoned cars around to take gas from!
Rope - Rope may be a good idea because you may need to do the following... tying yourself up when you get bite, tying others up, tying a door shut, making traps... Who knows?
Night Vision Googles - A good idea when wandering in the dark, hard to find but hey... They are well worth it
Watch - Good for telling what time you should start preparing for the night, also good for figuring time to meet up with your group
People - Especially important for the apocolaypse, they may be more mouths to feed but protection in groups is your best option. I would suggest finding people at the beginning, when they aren't crazed from being constantly hunted by zombies and when the good people are still alive
Fishing Poles - Good for when food is low and cans are gone.
Hiking Shoes - Some type of shoes that won't wear out and isn't heels or flipflops, something that will surivive wear and tear and good for hiking up mountains or running.
Hand Sanitizer - You may not have time to wash your hands but you can just squeeze of this on and rub it in. Sometimes better then soap
Can Opener - Better then using a knife that's been through who-knows how many skulls
Blade Sharpener - Well lets just say a dull blade may be more dangerous then a sharp one
Radio - May only be useful for a few months but two way radios are great, or walkietalkies! Great for speaking to group members when seperated
Zip Ties - Good for tying up others, fixing things, creating traps and more.
Body Armor - Light weight armor may be the best, something thin and easy to breath out of. Riot gear is heavy and stuffy but good for when you get jumped, it protects you from those infections teeth and hands but also limit movement at times. May help stop a bullet as well
Local Map - You will need this to see good scavenging buildings, posible bases and terrian