Transistor radio and headphones
batteries
crowbar (relatively light weight, can be used as a bludgeon, and can be utilized to pry open doors or clear out debris
a hammer (Not too useful for combat since it has a short reach, but can be used to fortify doorways and windows)
a box of nails (a small in order to cut down on weight, other nails can be taken from structures or raided from tool sheds and maintenance rooms.)
Food
Hunting rifle and ammo
Pistol and ammo
Three knives (all at least with 5 inch long blades, one non-serrated for killing zombies, another non-serrated for handling food and a backup for if the zombie-killing one breaks, a serrated knife for utility purposes and a last resort)
A backpack
A sleeping bag (I have a really small compact one)
Hiking boots
Two extra pairs of socks (changing clothes will not really be necessary in the savage wastes of a zombie apocalypse because everyone will be disheveled but clean socks will help ward off diseases like athletes and trench foot).
A flashlight
Maps of the surrounding area
A compass
A poncho
Pocket knife
A first-aid kit
Sunglasses
A bandana
A hat
A pair of Binoculars
A lighter
Two quart-sized water bottles
Water purification tablets (Maybe a purification pump if I can find one)
I will also scavenge some more supplies and restock from prime locations such as gas stations and gun stores if they haven't already been looted (and if they have there's always something useful that has been overlooked)