Everyone should have one:
Tent
Sleeping Bag
Air Mattress
Pillow
Any Extra Blankets
Towel/Washclothes
3-4 Summer Outfits
3-4 Winter Outfits
Winter Coat, Boots, Gloves
Hiking Boots
Books/Paper/Pens/Pencils
Few items of importance (pictures, trinkets)
Pets
Soap/Shampoo
Any Non Pershiable Food
Toilet Paper
Seeds
Bucket
Frying Pan/Pot
Needle and Thread
1 Weeks worth of food and water
1 set of dinnerware per person
20 empty mason jars
pocket knife
scissors
first aid kit
tweezers
hat
matches
Candles
Flashlight
Bow, not Crossbow
I believe the following are great additions to the above gear. A handgun in a standard caliber (9mm or .45, .40 will do but not as ubiquitous as the others mentioned. I prefer 9mm since its the most popular, you can carry a bunch and with modern +P hollowpoints they flat out get the job done), a heavy well made sheath knife (more for skinning animals once canned goods run low), a multi tool in belt sheath (gerber preferred) and a lightweight prybar to open doors that don’t want to or as use as a bludgeon as necessary. I also think a lighter leather work boot would be better overall than hiking boots. Hikers tend to be heavy and bulky, not so good for running or climbing, but a mocassin styly hunting boot protects the ankle but with the shofter shank material has the give for more comfortable walking (mine are Filsons). Old school style never goes out of style.
unless absolutely necessary I would try to stay away from Chainsaw’s and baseball bats. who knows what the blood splatter might cause if it gets in your eye or mouth and in your bloodstream. stick to projectile weapons. and if zombies can hear then your going to want something quieter, maybe compound bow or crossbow. with lots of arrows and bolts. if all you need to do is put a bullet in the head .22 will work great its quieter than a lot of guns, pretty accurate, a lot easier to pop off multiple shots that are more on target than with a 9mm and you can have rifles and pistols with the same ammo. and there is lots of .22 ammo. but a 9mm or .45 are great to have too. cant ever have too many guns in a zombie apocalypse. and a good long range rifle with a good scope.
oh and in the list I didnt see rope. havent you seen Boondock Saints?
and everyone should watch the tv show The Walking Dead. lots of good tip ideas you can get from there.