Suppose you are settled on WAR now, do you only level a tank class levelled at max level for the necessary end game content & farming? Or should you focus on a DPS class? So advice are ready for you if you get Heavensward on your handy.
Here are bunch of things.
First off, if you really want to get a feel for a class, do Palace of the Dead. It's unlocked at 17ish in Quarry Mill. You have a separate exp bar while instanced that levels up very fast letting you try out abilities as a level 60. This is also a fast way to level up dps classes. There's no need for a tank or healer so you get faster queue times than a dungeon. Also, it helps work towards getting a nice level 60 weapon once you get there.
It is ideal to go through the MSQ as a dps since you get a lot of experience from them while not needing to queue for anything (albeit when story makes you to advance). However, it's not necessary. There's plenty of ways to level up as dps without having to sit in long queues (like potd). So if you want to main a WAR, then go ahead and main your WAR! If anything, it'll help you get through your MSQ with faster queues (assuming you're comfortable going through content for the first time as a tank).
If you do keep playing WAR, take a quick break to level up GLA just a little bit more. At around level 22ish you get a move called Provoke that is incredibly useful for tanking. Might as well get it asap.
Remember that some class are built based on the fact that they do superior burst to anyone else but take a while to ramp up so to speak. It's sure that you're still going to need to work on your level 60 rotation when you get there and start doing things. But it's hard to fully judge a class when you're at a low level. It's hard to judge a class until you've unlocked your level 60 skill. So you can sit there doing things outside of potd and you still aren't going to develop any of the skills that you would have if you're 60.
Just advice for reference. Then you get other ideas, you can share with us. Or you get interested in the advice or tips we provide, you can have a look. By the way, our online store is a safe place to get FFXIV gil as well as power leveling.