Equipment basics. This is what you'll want to have before the event even STARTS, even though the weapons can be procured shortly after as well since they're pretty much only useful for a zombie outbreak unlike the other stuff. The other stuff is things you should have even if the zombie apocalypse DOESN'T happen.
(If you're a republican, you might very well consider a rifle or handgun useful even when an emergency doesn't happen. But if you're not a gun nut, you are excused for not owning them. Having a basic familiarity and knowledge of common weapons will help, however. If you live in the US, procuring weaponry will be easy enough so you can be excused doubly for not owning them. If you can't even own weapons at all, make sure to get them ASAP after the outbreak)
Hatchet, Knife and Crowbar. The hatchet and crowbar are weapons as well as tools, the knife is strictly a utility tool. Don't try to take a zombie on with it. You'll die.
Rifle. Something bolt-action, or at least single shot. This encourages good aim, the weapon type has the optimal braining ability, and if you're close to a zombie you shouldn't use a rifle anyway, so an assault rifle is suboptimal. Not to mention assault rifles need a lot more maintenance. Do not fire at targets above 100 meters away without extremely good reason. Targets above 100 meters away are better off ignored. I suggest 30-10 meters, to maximize aim. A single bullet wasted can very easily mean your bloody, fast, death.
Handgun. A pistol is preferable to a revolver if you are skilled enough, if you are not, a revolver is easier to use by far and is thus the better choice. This is for mid-close encounters (under 10 meters) only. For any distance above that, use the rifle.
You'll want a heavy, very sturdy backpack. Military issue is preferrable. If not, outdoorsy hiking types. Ensure that the backpack can be removed from yourself with extreme ease, a mere shrug of the shoulder in the right way should do it. This ensures that if you get grabbed, you can ditch it immediately.
For food items, anything that can be eaten cold and lasts in room-temperature storage is a must. A week's supply at the very least.
At the first sign of an outbreak (or any other type of disaster), draw massive amounts of tap water up into storage. It is not suggested to keep liters upon liters of water around constantly, but empty containers, well..you have some of those around, don't you? Note that WATER is what you want. Nothing alcoholic, milk, juice or soft drinks. Milks and juices go bad fast, alcohol is plain out, when the apocalypse starts you are going to stop all your vices, cold turkey. Soft drinks aren't preferrable due to their dehydrating side-effect.
First Aid. You'll want a full first aid kit. If possible (I say this a lot, but they make very sturdy stuff), military issue. Bandage, antiseptic spray, burn cream, medicinal alcohol, cotton swabs. Those are the basic items a first aid kit must have. Above that, you'll have to consider if you want to add to your backpack's weight because you can't handle bugbites and indigestion. Heavy painkillers, morphine being ideal, are very good to procure soon after the apocalypse, if you can somehow find a hospital (or preferrably, pharmacy) that isn't overrun with the undead.
You will be unable to use a car very early on, because the roads will be blocked up very badly. Ergo, going by foot or bike is optimal, until you can find something very heavy to aid clearing vehicular debris on-the-go. (A military troop crawler, AKA an APC, is ideal. If not, a bus or truck with hillbilly armor works too. Certain construction equipment is useful as well, but they usually don't have the pure amount of storage space that APCs or busses do.)
As for other survivors you meet, once you get to a safe place to spend the night, demand full stripping and medical inspection from every one of them (and yourself of course). Anyone with bite marks must be tied up overnight, if possible to a radiator or something else that won't let them go off biting you in your sleep, and then ditched in the morning. If the other survivors refuse, leave without them.
This goes for your friends, girlfriends, wives, boyfriends, husbands, parents and children too. Anyone gets bitten, they are to be abandoned. There's nothing you can do for them unless you are willing to waste ammunition. It sounds cold, but if you do not act cold, lose your humanity for now...you will die, and lose it forever.
The ideal place to go is very rural midwest (if in the US, similar rural farming areas if not). You'll want a place that can be set up with triple layers of mesh wire, very sturdy. You'll want an unlimited source of water, such as a river or an area with several underground deposits of water (this is why US midwest is ideal). You'll want a lot of farmland, and not a single other house in sight. All the farmland and surrounding area of the house you are planning to use will be, as previously stated, surrounded by at least three layers of wire mesh fences, and place them down REAL sturdy. If you can break through them by driving with your truck, it's not sturdy enough. The entire fence-line be replaced at least once a year.
You'll want to learn farming. And fast. Enough for personal survival, a decent underground stockpile (you'll want to dig an underground storage area, this will make cold storage in winter easier) and anyone else that gets there.
Procure a ham radio or even better, an internet source. Reach any survivors you can, any way you can. Tell them you have a safe place. Make extremely sure that every single person who comes to your fortress will get a full medical examination. People with bites will be turned away. At gunpoint if need be. Anyone who does not have visible bite marks will be placed in a storage area for five days, and treated very well during the time. When that time has passed, if no obvious condition deterioration has happened, they're free to join you.
Explain beforehand what will happen, of course, and why. (Non-injury infection) You're not the bad guy, you're just a survivor.
You'll want to find someone with technical knowledge, to place some sort of infinitely renewable energy source (wind energy, water energy, etc.) at your camp. If at all possible, procure electrically powered agricultural equipment. If done correctly, your camp should be almost completely independent with no need to venture out for supplies.
If you do end up venturing out, you will get supplies in this order: Necessary, useful, doubles of necessary, doubles of useful, wanted.
Necessary being things that you need, such as replacement parts for agricultural equipment or replacement wire fences. Replacement first aid supplies too.
Useful being things that could come in handy, such as weaponry, first aid supplies if you're not running low, computers if you have an internet source, etc. Condoms and clothing also falls under here. (unless you're all running around only wearing socks, in which case clothing gets promoted to necessary. Condoms are never 'necessary'.)
Doubles of those two is self-explanatory.
Wanted, if you STILL have space over, will be things like entertainment (sports, games, computers if you don't have an internet source, etc.), liquor, cigs, whatever.
NEVER. EVER. EVER. FOR ANY REASON. go out on a scavenge run only for wanted things. EVER. No, I don't care how much you want a drink/smoke or how bored you are. You are not leaving camp if there's nothing that is needed.
If anyone disobeys that rule, they are free to leave, but upon returning they will be treated to a full medical examination, including put into the holding pen for another five day period. And they cannot use any of the group supplies, such as the troop crawler/bus/whatever. If they seriously think a bit of liquor is worth all that, then it's their head. They'll be gone soon enough, permanently, and the people with patience and brains will be left alive. This is how you need it.
Another extremely important rule: Guns are for zombies only. Anyone holding or using a weapon on another person, for any reason, is exiled immediately. Tempers are sure to flare, but life is extremely precious, and more importantly, tempers flaring is always how the people in the films die. If you can't stay together for pure survival, then you WILL die.
There. That should keep you ticking until they've all rotted to dust in 10 years or so. Until then, grab the nearest person of opposite gender and repopulate the earth. We'll need it.