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Speaking as an expert in zombie apocalypses, here are my thoughts.
Classic chainmail is far too heavy to be practical. However, the shark suit you mention is an option. It's called a Neptunic suit (they hold the patent). Again, though, it's still heavy - keep in mind that it's meant for use underwater, where mobility is not such an issue. Also keep in mind that it's not the bite that gets you, it's the fact that you have broken skin through which you're infected with a "virus" which is transmitted through bodily fluids. Armor decreases the likelihood of your skin being broken - it doesn't eliminate it. Where pressure is applied to the mail, the skin can still be broken. Because the links are porous, the fluids can still get through them - and into any opening, whether it's a cut or, say, your eye or your ear.
There is a bigger problem, however. Assume that the zombies cannot break through the mail with their teeth. This does not suggest that they're going to simply give up and go away. Nor are you likely to be able to move quickly enough to free yourself once they've got you. They're mindless creatures and will just keep trying. Being swarmed and essentially dogpiled by a hundred undead and being unable to escape, slowly suffocating under a mass of bodies trying to break through your armor, does not sound like a pleasant way to die. Of course, it's likely that you'd accidentally ingest some virus at some point and then everyone else would have the distinct pleasure of meeting a zombie fully garbed in chain mail.
Ime, the best armor is a reasonably thick leather, like treated lambskin. At a good thickness, leather is pretty biteproof. It's also not porous. Most importantly, it's easy to move in. Remember, kids - if they can't catch you, they can't bite you.
As for swords.
Most people assume, based on videogames or movies or whatever, that a shotgun is the best anti-zombie weaponry. It is effective at blowing the heads off of zombies. Unfortunately, they fail to take into account two important things: splatter, which may be a bigger or smaller problem depending on how the virus is transmitted, and ammo. Not running out of ammo so much as ammo weight. For every dead zombie you need a shell. Try carrying around a bunch of shotgun shells and you'll quickly see the problem.
Swords have their own drawbacks. The main one is obvious: you have to be up close and personal. Not only does this bring you within prime biting range, it creates its own splatter issues and limits your field of vision; while you're cutting one Z's head off, another is coming at you from 8 o'clock. In the chaos, you probably won't hear him until he's pretty close by. Another issue is fatigue - the first 3 or 4 Z's might not be an issue, but try swinging a sword constantly for a half hour. For this reason alone, a sword is only really effective when dealing with very small groups - and you may not know how big a group is until you're too close in to get away. Other normals can't shoot at the zombies while you're in melee with them, or they risk hitting you. Oh, and before I forget, you actually need to know how to USE a sword, which I can pretty much guarantee you don't.
Some people may want to carry a sword around, but I would not be one of those people. What you want is a rifle with easily carried, widely available ammunition that (and this is the most important thing) is as close to 100% reliable as makes no odds. The thing should be able to fire when encased in Jell-O.
Costco is good, but has its problems. It's hard to defend something like that - there are a lot of access points. It's kind of like holing up in a mall. One of your main issue is other survivors trying to get in and causing perimeter breaches. Also, no matter how many cans of tomatoes your group has, somewhere down the line you're going to run out of something crucial to survival.
There are two schools of thought. One is keep moving - swarms can't trap you in a stronghold if you're constantly changing your location. So, you get a well armored, smallish vehicle with living quarters. This is never the immediate solution people come up with because human beings like a nest, something they can get familiar and comfortable with. Personally, I'd rather be able to haul ass as quickly as possible and be a few clicks away in ten minutes.
If you really do want to go for a fixed base, here are some possibilities.
a) high off the ground with limited means of access but an escape route. Think "tall building with two locked, enclosed stairwells leading to an enclosed underground parking garage". If you can sterilize that and it's secure enough, great. But the inevitable problem is these things only really exist in high-population centres. Cities are best avoided.
b) renewable sustenance. I.e., hydroponics so you can grow your own food. A purified water source and rain collectors. Solar power.
c) As small as possible. There is no reason to draw attention to your base so that other desperate survivors who haven't planned as well as you want to raid it, take it over or whatever. If at all possible, you want to make it look like no one is there. Which is why steel plate and razor wire are a problem.
Imo, if you want the best stronghold, outfit a lighthouse. Usually, they're far from civilization and hard to get to (out on rocks just off shore). They're tall, and have an unobstructed view of the surrounding area so you can see problems coming. The coast is usually a high-precipitation area so you can collect water, and there are no trees to block any solar panels you might have (if you're really well prepared). And you can even rig up an escape method in an emergency - a zodiac or similar boat. Zombies don't swim very well.
To that point, boats are also suggested by some, but once you get one infected on there you're totally screwed, and it's easy for things to break down on a boat. Then you're stranded.
That's the benefit a lighthouse has over something like an oil derrick (which in itself is a much better plan than most places you could find yourself). Lighthouses are generally fairly close to, or connected to, shore. So, escape route 1 is by boat, escape route two is by land. For obvious reasons, you're more likely to use the boat, but who knows.
Fishing is a great way to get food, because it poses basically zero risk. The odds of reeling in Zack are nil. Hunting is much worse because you'll likely need to cover quite a bit of ground and it's thick foliage where you might not see one lurking, but on the plus side, there are generally very few people (and hence few zombies) in hunting areas. And, of course, you can always forage.
Really, though, like I say, you need to be able to grow your own food, wherever you're holed up. I for one would not hole up, I'd want a fairly large vehicle. If you look in the ski RV's thread on TGR there are some things in there that would work.
Why on earth would you need to grow it on the ground outside? Standard garden boxes would work perfectly well. There are plenty of indoor gardens. You don't need to feed an army here. Yes, you do need a reasonably sizeable lighthouse with some square footage, i.e. not one of the recently constructed ones. It would be tough to find one, so start planning now.
Here are a few examples of what I'd want...
I hope you've selected them wisely and everyone understands that at the first sign of infection they will be killed. Because that can be an issue - someone gets bit and tries to hide it, and bam, movie-style crisis. I wouldn't bring anyone I'm not willing to shoot in the face without hesitation.
Really, you want the zombie apocalypse to resemble a zombie movie as little as possible.