As mentioned in the recently locked thread, there is a set of (old) videos which do a great job of outlining Destiny's simple story plot... which is made not so simple by the game itself due to shitty presentation and intermixing of side stories.
The main story missions
After watching that video, the main story made SO MUCH MORE SENSE. And actually comes off as pretty decent to boot. The game fails to present contextual importance to the events as they happen... something that could have been easily remedied by a few more cutscenes at key moments.
The Rasputin side story
During my initial playthrough of the game, I was confused as hell because I couldn't grasp exactly what Rasputin was, and I was convinced he was the primary antagonist in the game... when really this was just a side story the entire time and completely separate from the main plot. Edit: It apparently doesn't have a satisfying conclusion? Can anyone here clarify actually?
Crota, Oryx & The Hive
I haven't watched this one yet... about to. Edit: Not bad. This has become Destiny's current main plot due to taking out Crota in DLC1, and facing Oryx in TTK.
Seriously, I suggest watching these videos if you haven't. They put things into context quite nicely.