New Tank Help

[Merkava]

This is gonna be a bit of TL;DR so bear with me as I hope this is a productive post for you as a new tank player.

Always play conservative as a learning Tank.
You always keep hearing about the meta and how top WARs are as much DPS machines as they are good tanks and about how people like to do humongous pulls in order to clear dungeons in 15-20 minutes. Well, the truth is that none of these tanks (the ones that are good at least) started by playing aggressively, they only did after they understood their class and knew well the encounter/dungeon before hand. You could ask any of the big names in Tanking now-a-days (like Xeno and Layla) and they will most definitely tell you that a tank starts by playing defensive and only start with aggressive tactics once they are familiar with their skills and the challenge ahead. Heck, if you view this MogTalk show where both Xeno and Layla speak, they actively stress this various times. So really, it's OK to play defensively all the way until 60 and then worry about optimizing later. If you run into an asshole in DF then tell them to screw off and vote-kick them, I can guarantee that chances are that you'll win the dispute as most people are more inclined to kick an annoying DPS or healer than a defensive tank. Heck, if you end up being kicked due to reasons (like a premade party) then screw it, you have super fast queues as a tank, you'll be back in a dungeon in less than 3 minutes.

Always level up via Dungeons
Dungeons are the best way to learn your class, avoid leveling via FATEs as much as possible. People might tell you about how it might be faster but going from 1-60 via Dungeons will make you a much better tank than leveling through FATEs.

Always upgrade your gear
This is insanely important as a Tank, there are various options for upgrading gear. You gain some from the MSQ and dungeons offer gear as you progress. But what happens when you get RNG screwed and/or the next few MSQ's don't offer a viable gear upgrade? Well you should be aware that every 5 levels there are buyable NPC bought gear, I do not recommend using the market board as from (my) experience they tend to have gear horrendously overpriced when compared to what you'd get from an NPC. Where can you buy gear upgrades in case you are falling behind level wise? Well here is a small list of places where you can buy upgraded gear (they coincide with levequests):
lvl 20-25: Quarrymill (This is a bar located near the Upper Path)
lvl 25-30: Quarrymill (The town itself)
lvl 30-35: Costa del Sol
lvl 35-40: Coerthas Central Highlands (Where you warp in)
lvl 40-45: Coerthas Central Highlands (Whitebrim Front - This is the fort on the north-west corner of the map)
lvl 45-50: Mor dhona
Always make upgrading your weapon the highest priority as the stat "Weapon Damage" is a huge modifier in your damage (helping a lot with enmity) as 1 point of Weapon Damage is roughly worth 10 points of Strength. Also remember to use the "compare equipment" sub-menu before upgrading (right click on the item) as Green items (or maybe pink) can have higher stats than shop gear of higher level.

Ignore the STR and VIT debate for now
In line with my first suggestion, this sort of stuff you worry when you are level 60 and working on becoming an exceptional tank. So it's OK to go full VIT for now and then later work on the vastly superior STR builds (and when I mean later I'm talking post-60).

What are the best cross skills?
The best cross skills for WAR are hands down...
Flash (lvl 8 Gladiator): Get this skills ASAP, this is insanely useful at low levels and remains useful all the way to level 60 as it gives you an extra source of AOE enmity and some use for your MP.
Convalescence (lvl 10 Gladiator): 20% extra heals? This skill is another awesome skill to have.
Provoke (lvl 22 Gladiator): A must for any tank, this allows you to tank swap on more difficult encounters and recover from mistakes easily in any fight (IE. you die or you miss a mob).
Internal Release (lvl 12 Monk): 10% Extra crit and on a short cooldown, why the heck not? It's an awesome skill.
Awareness (lvl 34 Gladiator): This skill makes you immune against critical hits, its direct usefulness in battle is questionable (aside from certain battles like Shiva) but it is amazing when combined with Raw Intuition. This skill is great but not really mandatory until Heavensward.
Second Wind (lvl 8 Monk):A self heal, nothing amazing but why not? This is mostly used in encounters where flash isn't necessary (IE. Trials). You just replace flash as the encounter requires it.

As you noticed an extremely important number of skills come from Gladiator so leveling them to 34 is kinda a must. Your Cross Skill should look something like...
Flash/Second Wind, Provoke, Convalescence, Internal Release, and Awareness (in that order, IMO).

There are no useless skills
One amazing thing is that Warriors do not have a useless skill in their toolset (some more situational than others, like Holmgang). A small thing to note is to always find someplace to use a skill you gained, if you're letting it sit on your hotbar with no use at all then chances are you could be doing better. Take Brutal Swing for instance, your stun skill, you might be inclined to only use it to stun enemies (which is fine) but what happens when you're fighting a small mob where stun is irrelevant? or a boss that is immune to stun to begin with? Why not use it? It is a DPS boost. Be creative as you experiment with warrior, don't be afraid of making mistakes. Try to fit every skill you get somewhere.

The path to excellence is full of failure
This is more of an advice you should consider once you hit 60 and are striving to become a better tank. As you get used to your tanks skills and your "safe" HP threshold you will make mistakes, don't let this discourage you as you might be humiliated a few times, namely with elitist players. Keep going and you'll be psyched when you're clearing content as a pro-WAR, with people are throwing coms at you left and right. You will fail and every failure is bound to make you a better player, as long as you learn something from said failure.

Once you hit lvl 60 and want to become a better tank I recommend Xeno's tanking guide as it is a great resource for improvement. But note that I recommend this once you're level 60 and beyond, so bookmark this and keep it for future reference, don't you dare try to become an aggressive tank from the go, you will fail horribly and look silly.

I hope this TL;DR was somewhat helpful.