In EVE the Amarr and Gallente both almost exclusively run armor tanks in their larger ships, and some Minmatar ships do as well. As you get into higher end missions in Battlecruisers and Battleships your ability to tank be one of the primary factors in your ability to make money, and not loose ships worth tens, if not hundreds, of millions of isk. Bad tanks cause a lot of grief to newer mission runners, so here is some basics that could get your tank ready to roll.
The Do Nots and Myths of Tanking:
Hey, we like our shields and our armor, so let's repair them both! Even better, we want to last a long a long time so lets load up on insane armor and shield hit points! Both of these sound nice, but both of them miss the two most important aspects of tanking, defense and capacitor stability.
Defense is a statistic provided by your shield and armor repair units, as well as your shield's recharge time, which is quite literally points of repair over time. For instance an armor repper could be repairing 240 damage every 2.5 seconds. Now a common misconception is that this should be considered "healing" of some sort, but it isn't when you're under fire. That is instead the amount of damage that can be completely negated every 2.5 seconds. So if you took a missile doing 100 damage every second, your armor would only really be taking 10 damage every three seconds. Only two reppers can be active on a ship at any given time, so for our example 480/2.5 would be the new defense.
Let's say that 480/2.5 isn't good enough anymore, your taking 300 damage a second and that defense of yours just can't keep up. You can try and buffer that out, but that only extends the amount of armor you'll eat through before you warp out which isn't a true stable tank. You need more defense, but you can't fit any more reppers, what to do. This is where your ship's resists come in, you can't increase defense, but you can decrease the damage you have to defend against. If you're taking thermal damage, your ship may have a base resist of about 20%, and your taking 300 damage meaning they're actually throwing 360 damage at you every round. Throw on a thermal hardener and add 50% resist to that, 70% resist now and that 300 damage is now 108 damage. Even if you had only one repper on only 20 damage would make it through your tank.
So why not put a shield repper and an armor repper? Because one is going to have high resists and the other low resists. In that same example, but with a 240/2.5sec shield repper, and same on armor, your shield repper is going to be fighting against 300 damage a second and being completely overwhelmed, while about 20 points every three seconds is still going to get through your armor repper when it's done with your shields. Compare to two armor reppers which could sink all of the damage and you would never have to leave system at any point.
On top of that, you want to have a stable capacitor. Being cap stable requires a lot of work, lots of cap rechargers, and CCC rigs, or sacrificing massive amounts of cargo space to cap charges which become increasingly ineffectual. Missions are even more cap critical than PvP, since a PvP rig can get by lasting a few minutes since most engagements small enough to prevent your getting a chance to take a breather are only going to be a few minutes anyways. Missions however can take an hour or longer, and having to return to station to recharge cap is only going to make them longer. Using our above examples, the armor tanker with two reppers has the option of sticking to their one repper while the situation is controlled and decreasing dps by taking out ships, but they also know their tank won't break if they suddenly have to deal with a spawn doling out an addition 200 base-dps or 60 actual-dps. The split repper has a problem though, if they turn on their shield repper they will actually take more damage, and if both of them are on it'll eat through their cap at an accelerated rate. If they leave the shield repper off, then it's just wasting a space, one that would probably would have gone to something that could make them cap stable.
The Does and Facts of Tanking
So how does one tank a large ship for mission running? Ship Bonuses, Hardeners, Reppers, Cap Rechargers and Capacitor Control Circuits. But first our ships, I'm going to focus on Gallente and Amarr, since I know they regularly armor tank. BC wise this means the Brutix, Myrmidon, Harbinger, and Prophecy. The Brutix and Harbinger have roughly the same basic concept behind them, you'll want to get in fast and do lots of damage since you're probably going to get hit a lot. Even with ranged weapons you're going to need to move fairly quickly on occasion to get within range of ultra long range enemies. The Harbinger especially, since it doesn't give you any sort of boost to your tank except reducing the amount of cap drained by your weapons. The Myrm is a drone boat, so simply adding a drone link augmenter should, with good drone skills, set you up quite nicely to fight at any range. With the Prophecy, you have resists bonuses based on skill level, so you should be able to very easily set up a very strong tank, just add a bit of speed to close range when needed.
BS wise, you have the, Dominix, Megathron, Hyperion, Armageddon, Apocalypse, Abaddon. The Hyperion and the Abaddon are probably the only ships with significant tanking advantages, the others are all based off the idea of kill it faster than it kills you. However, the Hyperion will give you much better defense at high skill levels, and the Abaddon will provide much better resistances at high skill levels.
So what is a basic fit for mission tanking? 2x tech 2 reppers, medium for a battle cruise, large for a battleship, 4x tech 2 hardeners, I'll get into which in a bit, and a full mid row full of tech 2 cap rechargers, with two or three capacitor control rigs. Battleships are best with tech 2 rigs, for BCs it doesn't really matter that much. The most important thing about rechargers and CCCs is that they have a cumulative effect, one won't do much for you, two does slightly better, three is nice, four and above each one starts really having an impact.
This mission tanking guide will give you exact damage types for all of the enemy types as well as a hardener breakdown for each one. For the missions I run in Gal space, I usually need to know Serpentis, 2kin/2therm, Amarr, 2em/2therm, Angel, 3exp/1kin, and EoM/Gursita, 3kin/1therm. If you have additional low slots, I highly recommend Energized Adaptive Nano Membrane II, or a Damage Control II. The EANM will increase all of your armor resists that extra little bit to really solidify your tank, the Damage Control will assist your tank a little, slightly increase your shield buffer, but most importantly it'll add about 60% resistance to all of your hull resists, giving you time to get out if you start entering hull damage.