This assumes you've read the wiki to some extent. If you haven't, well... here you go-

http://wiki.spiralknights.com/Defense
http://wiki.spiralknights.com/Armor
http://wiki.spiralknights.com/Abilities
http://wiki.spiralknights.com/Firestorm_Citadel
http://wiki.spiralknights.com/List_of_prestige_missions (See danger missions)

Generally you're going to want to choose armor to meet these goals-

1.) A general use set that you use on every level; i.e. lots of bonuses for whatever weapons (Chaos, Black Kat)
2.) More specific sets for particularly challenging levels that you'll want to complete-
2a) Heart of Ice = Freeze +9 (Black Kat)
2b) Compound 42 = Poison/Fire +9 (Dragon Scale or Armor of the Fallen)
2c) Ghosts in the Machine = Shock +9 (Seerus)
2d) Firestorm Citadel = Fire + 2 (Chaos, black kat, seerus, volc demo, vog)

In parenthesis are the generally accepted set(s) that people use to cope with these situations. It doesn't matter that you choose these sets so much as that you choose sets that get you the correct status resistances and bonuses that you need based on your choice of weapons. For instance, if I have blitz needle, I probably want charge time reduction.. so I have to use seerus or chaos to get that but I could also use vog and just bring trinkets. If you want to bring vog and trinkets I'm not going to stop you.

Armor worth talking about

Chaos Set

Chaos is probably the most crafted armor and with good reason- it gives a TON of bonuses at the cost of a few status resists, meaning for most levels, which do not feature too much status anyway, or for levels where you can mix it with status resistant armors, or for when you can get UVs, chaos is pretty much unbeatable.

One thing to note about chaos is that it's relatively dangerous when you lack UVs, heat, health trinkets etc. and are new in general. You may wish to ease your way into chaos by crafting one piece of vog and one piece of chaos, or even by starting with vog first. It all depends on your skill level, internet connection, and how beefy your machine is. Regardless, once you can get shock/fire UVs onto chaos you'll be set for life and things like skill and internet speed won't be as big of obstacles because hey, you have super armor.

Black Kat

Black Kat is expensive, but worth it. It's literally the only armor that really one ups chaos, and it's paywalled off.. but that's ok, because we have 3* black kat items that do just about the same thing as the 5* in terms of offense, which is why you want the item in the first place. Pick up the 3* sets whenever the event is taking place and you can afford to, and when you find a book or so, eventually, think about upgrading your cloak and keeping a cowl.

In terms of use it makes all other freeze resistant armors useless, because why would you want to focus on defense when you can focus on defense and offense? For this reason, it's best to avoid all armor with freeze resist. You'll have black kat at some point.

Seerus

Seerus is the most defensive elemental gear piece, has fire and shock resistances, and grants gun buffs for ctr and asi. This is why people use and love it- it turns you from a glass cannon into a slightly less bombastic normal cannon, or just boosts your defenses and offenses a bit in general. The only downside is operation crimson hammer, which must be purchased. This is also an upside, since the bomb and sword you get there are both incredible items in their own right, making it one of the best investments a knight can make.

Volcanic Demo Helm

This is a less obvious one, but if you plan to bomb it shouldn't be. If you're doing FSC you'll want either shiver or blitz or both, probably more on the blitz side but bombers aren't common and shiver does help out quite a bit regardless of whether the Vanaduke fight lasts 30 seconds or 30 hours. Bomber is a strong role and this helm is basically the bomber equivalent of Seerus. If you lack guns and have bombs you should probably be using this helmet for FSC.

Vog

Vog could be considered the sword equivolent of Seerus.. but it doesn't grant you ctr, so it's pretty much not. Vog is good however, because it's easy to craft and widely useful. If you're going all swords and lack bombs and guns then it's your best bet by far. You can also pair it with seerus or itself or volcanic demo to fire in C42.

Dragon Scale Set / Fallen

Dragon Scale Set is pretty much only good for compound 42. That being said, it turns compound 42 from a challenge into kittens, just like that. When you have your general use armor, dragon scale set is a pretty nice project to make, since it can bring in a good amount of free-ish prestige every fourth day.

Fallen is similar except instead of being useless offensively it packs a slight punch and makes you take a much larger punch. It's also not bad as a substitute for vog in Firestorm Citadel, and is particularly beginner friendly there. If you're really progressive you could plausibly go fallen+seerus to cover C42 and FSC in one fell swoop, though this is certainly the path less taken.

Mercurial Demo

Mercurial Demo is good for its high shock resist, decent actual defenses and most importantly shock resist. If you want to be fully shock protected, this is a pretty good option.

The 36 million gunner armors

These are good for filling in holes with the above. Lets say you don't want seerus, and are looking for some armor with fire resistance that benefits your guns. Well one of the sets will have that. Generally speaking, you want the pure damage set that gives you one bonus to each asi, ctr and damage category as opposed to the pure damage vs X armors, since damage vs X is kind of unreliable.

Those other armors..

I'm talking about armor like chroma, radiant silvermail, plate, stuff like that. No, these aren't 100% useless, but they're relatively underwhelming and not worth talking about or crafting unless you plan to collect armor. Lets take for example volcanic plate set. On fire levels, you can build the following-

volcanic plate armor + volcanic demo

This is a VERY potent set for the third round of the gauntlet, which features fire, gremlins, and various construct. But outside of that, it's pretty garbage because you raise your bomb slightly slower and massive amounts of normal, elemental and fire resist probably won't apply.

So yes, you can use these sets and they'll work to do what they say, but have fun heating them for that one tiny scenario.

Order of Crafting

1. Start with your general use set, which is probably going to be chaos or chaos and seerus. Getting this set will let you do most levels competently.

2. Build for the levels Firestorm Citadel and Dreams and Nightmares

3. Branch out into the other sets mentioned, so that you're prepared for anything

4. Goof off and craft volcanic plate if you still want to

Unique Variants

If you have a set to resist a status, you'll want to get at least a low in that status on that item. For instance, if I have dragon scale set I'll want at least lows in fire and poison on the set, so that I can fully resist whisps and other low statusing hazards. This is the power of those sets.

For your general use set, you'll want fire/shock resistance, so as to further resist the worst statuses. Freeze is also a bad status but you have black kat to deal with that for you.