New player with a couple questions

[Niwashi]

You can leave ALL the sidequests for later classes to help you leveling a bit.

Well, some sidequests unlock content or features. They could still be with a different class than the one you do the main story with provided you're alternating to level both classes up near the same time, but the ones that unlock features shouldn't be put off for too long. A good listing of how different features are unlocked can be found on this wiki page. Any other sidequests, though, that are neither part of the main storyline nor listed on that unlocks wiki page, can as TheTen mentioned be put off to use while leveling later classes.

Your biggest EXP gain is currently dungeons (starting at lvl 15), but as a DPS, you will have long wait times.

And the DPS wait is likely to be longer than ever when everyone is trying to level their new ROG/NIN. When that first comes out will be a great time for anyone wanting to level a tank or healer class to do so.