I wrote this ages ago for some reason and hey, why leave it in drafts forever?
A lot of hardware shops and builders' yards will have reasonable supplies of very hard-wearing gloves, steel-toed boots, face masks and possible even welding masks. This is to say nothing of the huge amounts of building materials. Garden centres will be another good source of protective equipment, as will certain types of factory. Usefully, both the latter tend to be built in relatively isolated places.
These and similar businesses also have trolleys of various kinds, which will be invaluable for transporting stuff. Forget cars.
This will probably sound silly, but supermarket trolleys are well worth acquiring in huge numbers; they are amazingly useful and flexible. You can store things in them. You can transport them easily. You can strip them for wheels and spare parts. As storage, they can protect valuable items from quite a few types of wild animals - dogs, foxes, sheep, basically anything than can't wriggle through, climb over or tip the trolley. Their slick metal frames are hard for many animals to climb, so even rats and cats will struggle to get through.
But that's not all! Grab every trolley in sight and and circle them into an instant zombie-proof fence! They should be able to slot together into a very large closed circle. They're far too tough to break with normal force. They don't tip easily (especially in a line, where the weight is multiplied and anchored at many points), and too high for zombies to simply blunder over. Only zombies intelligent enough to actively climb objects will get past these. If you're worried, pop padlocks, cable ties or just lots of string to link them on the inner side, so the zombies can't try to slide them apart and undo the circle.
You can transport kids in them safely, at least with a bit of adaptation, and they're also great if you get the chance to loot some poultry, or even the odd sheep or dog - it's potentially much faster than trying to lead animals along.
Dogs aren't a great bet for zombie-surviving, though. They need meat to eat. For watch purposes, you're probably far better off trying to keep poultry. Chickens can make plenty of noise, while geese are famously good sentries (ask Rome).
While you're at the builder's yard, grab pallets. In fact, grab everything. But pallets and their pallet-lifts are very useful in general. Get pipes, too. You can do an awful lot with pipes, valves and taps, in terms of making and fixing stuff. Rubber and other sealants? Yep. Glass? You betcha. With glass, pipes, rubber sheeting (or equivalent) and some containers, you have most of what you need to get water and grow crops. They might not be nice crops, but hey.
Did you know you can run basically self-contained aquaponics by combining crops with fish? Pop round to the pet store too.
There are some other, weirder options you might consider. If you have access to a very large supply of transparent plastic boxes - like those storage boxes for keeping things in the attic or under the bed - then fill 'em with sand or pebbles and you've got a pretty much impregnable wall (stacked two or three deep and six or seven high). Fill 'em with water mixed with strong bleach or something (to stop algae building up), and you've got a near-impregnable see-through wall. If you've got an opportunity to scavenge significant amounts of a town, you can probably find a decent number. Even rectangular ice cream tubs would do at a pinch.
Old tyre heap nearby? You can build something approaching a fortress out of tyres with earth rammed down inside them.
Despite the nonsense zombie stories like to suggest, there will be plenty of people surviving a conventional zombie-as-carrier outbreak, or even a waterborne one. Oil rigs and ships are full of people completely isolated from zombies, and many of those people have enormous expertise in the technical fields needed to rebuild society; there are also medics, geologists, and people with all kinds of interesting hobbies. Ocean survey ships, as well as any number of research stations, hold people with biological, ecological and agricultural training.
Zombies aren't like most other diseases, they require a bite to transmit the disease, which means lots of people in relatively isolated places are likely to be safe for a few days. And they don't have to be safe for longer than that, because of biology.
See, most zombies wouldn't last long at all. If they're rotting, they'll be devoured by insects. If they have any metabolic processes at all, they need water. Once water supplies shut down, zombies will mostly dessicate within a few days. Also, if they act as typically portrayed, they will accumulate untreated injuries and bleed out or succumb to secondary infections. If they don't have blood flow, they have no means of transporting oxygen to their cells, which means they cannot generate ATP to power cellular processes, such as the contraction of muscles, which means they cannot move at all. If they don't have any metabolic processes, they cannot physically move because that's how biology works and no, shut up, SCIENCE.
In other words, whether your zombies are living-but-mindless, or rotting-but-mobile, they won't last more than a week tops. And honestly, probably less, because they'll neglect important not-dying precautions like shelter.
You need only keep yourself alive for a week or so, and then venture out to reclaim the world, alongside large numbers of oil workers, ex-prisoners, the inhabitants of all those secret Antarctic research facilities, people attending spiritual retreats, quite a lot of islanders, and most of the population of North Korea.
If the zombie plague is insect-carriable, things are a little trickier. In this case, you will need to hide out long enough for all plague-bearing insects to have died. Most have quite short lifespans, so once all the zombies have rotted away and the insects' lifecycle is over, you should be fine. On the plus side, viruses and other pathogens are quite host-specific so only a few other species will carry the disease. That being said, in this scenario people living in high mountains and the poles, where insects won't reach, are really in with the best chance.
Supernatural zombies are a different matter. These may be capable of remaining active and largely undecayed for indefinite periods because they contravene physical laws.
Supernatural zombies are amazingly useful .
If you have a creature capable of indefinite mobility without the need of metabolic inputs (such as water or a source of glucose), you can construct something approaching a perpetual motion machine. You should (once you have constructed a suitable facility) strive to acquire as many of these zombies as possible. The exact construction required will depend on the behaviour and capabilities of the zombies, but a simple welded steel treadmill, impregnable to most zombies and possible to make with relatively available materials, should do the trick. There are undoubtedly more sophisticated machines available to a trained physicist or engineer.
The infinite supply of free energy provided by your zombie generators will allow civilisation to rise again from the ashes, indeed with a new and brighter future offered by the end of entropy and the abolition of fossil fuels. Zombies save the world, and humanity!