A good pair of boots to walk the endless wasteland-
If you have to go on the run, you will be glad you aren't wearing your flip flops.
Choose your weapon wisely-
(from what I have seen, an easily reached side-arm and a long range rifle are both vital. A gun? Hell yea. 10 guns? Even better. And a huge crossbow wouldn't hurt either.
Knife, brass knuckles and gun all in one!!! The apocalypse gift that keeps on giving!
I'm not a fan of cans normally but at times like these, be sure to scavenge any cans and dried foods you can. Anything that has to be cooked will only draw the zombies with the fire and smell of decent food. Another thing that is not well known is that you can grow a survival sprout garden in a mason jar. You can simply continue to sprout beans and eat the sprouts with no light and little water and they have a surprisingly high nutritional content, much higher than the actual beans or seeds themselves.
money won't be worth much in the post apocalyptic world but other things will be... like gas, seeds for farming, medicines, luxury food items, maybe even condoms. Not only will people be fearful of leaving their safe shelter for "date nite" but hell, who wants to reproduce in this new world anyways?!
Trauma Pak Quik Clot
Preferably someplace with a good vantage point to see the walking dead as they enter your zone. A moat around your fortress is a huge plus!!!
Tarps and Water purification tablets/filtration system-
Let's face it, even if you're safe initially, you're going to be on the run soon. Tarps can be used not only as a temporary shelter but also to collect rainwater. It's important to stay hydrated at times like these. You don't want to go through all your tequila on the first day, do you?!
A bad ass backpack-
with multiple compartments to separate all your crap. Because let's face it, it is going to replace what you used to call a "bureau".
The right tool to help you get stuff done-
And who the hell is going to have room to carry a whole toolbox?! Pick one multifunctional one and find a special place in your badass backpack for it. God knows you're going to need it.
A good multi-purpose military quality cord-
to help with securing equipment & shelters, making restraints, creating fishing nets and anything else you can dream up.
And who could leave their pets behind as zombiefood?!
These will keep your pets comfy while they're on the run with you...