3Fortify Your Base
Shelter, along with food and water, is one of the three main essentials absolutely necessary to human life. Just because there's no more room in Hell for the dead, that doesn't mean you no longer need a roof keeping your head dry. So you'd better get busy either finding or building yourself no less than an impenetrable fortress, and stay there until this thing blows over, right?
Not so much.
Putting yourself in a siege situation only works if there's the possibility that the invading force will stop. But you're not dealing with people here. Holding out against an army of people works because people can be reasoned with, they might have to leave to get supplies, or perhaps they'll just weigh the pros and cons of the situation and leave.
Not like zombies.
"It's been two months, so uh ... you guys need anything? Coffee? Blankets? No? Nothing? Brains? Oh, OK! Brains it is."
Zombies don't get bored or impatient, they need nothing to keep them alive (because they're, you know, not) and they're not really known for their logistic prowess: No cons will be weighed here. Food is a pro. You are food. You are there. So there are only pros here. They will wait for you forever. But you will run out of supplies eventually, and every day you stay put in your nigh-invulnerable bunker is another day zombies pile up outside. Zombies aren't a threat because they thin out gradually over time - they're a threat because they fucking multiply. Zombies beget zombies beget zombies, and they do their best begetting while scrabbling incessantly at your door for months on end because they can hear you crying inside. All "holing up" in a stationary location does is make the zombies want it more.
It makes them savor you.
2Conserve Ammo: Use Melee Weapons When Possible
The zombie apocalypse is a rough and tumble place, and most of us manage to rack up ER-worthy papercuts even at our current passive office jobs. In short: You're going to have open wounds, and exploding heads tends to be a bloody affair. So if all body fluids infect, blood included, then bites are the least of your worries. Consider this: For the sake of argument, let's pretend you don't spend your free time reading about zombies on the Internet and are, instead, a human being at peak physical condition. Now, go outside and find the nearest, smallest wild animal. Good? OK, now dive-tackle that son of a bitch and try to take a bite out of it.
How did you fare? Did you manage to get even a lick out of that squirrel
If yes, then holy shit! You really did that? That was just a hypothetical scenario. You're crazy as hell. Don't waste your time here, man. The zombie apocalypse is the least of your worries. The Devil is probably possessing your scrotum right now; you've got bigger fish to fry.
But if you didn't manage to get a taste of that woodland critter, well, that illustrates the point nicely: Grabbing an unwilling victim with your bare hands and taking a bite isn't easy. Things want to live, and they tend to move around a lot when you attempt to eat them, just like you will when grasped by a zombie. Just avoiding bites is not the problem. However, showering an attacker with your head-juice when it is bashing in your skull with a cricket bat is quite a different matter. That's a fucking cakewalk. Bashing in a head at close range means you're going to get blood everywhere; if you had so much as a scrape, now you're a zombie. It's much better to use up a bit of your ammo supply, rather than risk taking a crimson shower in skull leavings from the infectious undead.