If you're already annoyed by the scenario questline, just wait for the filler quests before Heavensward, lol. They've been cut a bit during the last patch, but they're still very, very extensive. But can't progress through the game (level up, yes. Unlock new stuff, no) without those.
You can play all classes/jobs on the same character. Just pick up a class quest to get a new class on lvl 1. Which class you currently are depends on your main hand weapon and, later, a Soul Crystal. So you don't level your character, you level your class (or job, "Fishing" is a whole class by itself for example).
This newfound knowledge will surely help me in PvP when I'm out there trying to surive and kite and hope other classes can't get near me easily at these lower levels
There is no open world PvP, nobody will attack you without you actively joining a PvP duty.