Hainiryun's answer is excellent.
I just also wanted to add that additional information around Bahamut (the huge dragon) continues to be revealed throughout the main story of the game, even into the current expansion. So don't worry if you get through the Binding Coil of Bahamut and still have a couple questions about how things fit together.

If you want to see for yourself how certain events played out pre-calamity around certain characters such as Nael van Darnus (the head of the Meteor Project), Archon Louisoix, the Scions, etc., you can find a few videos of the 1.0 cutscenes online. I think they're worth a watch, but I won't fault you if you decide it isn't worth your time.

One more note: Much of this game's lore is told as exposition in dialogue and cutscenes. While the game does have two (very good) lore books and a few handfuls of short side stories accessible online, almost everything we know about the world comes from information told to us in the story/stories within the game. Details are unraveled over time, with important lore either being drip-fed over the course of several expansions or dropped on you like a bomb out of the blue.

Have a safe journey, Uplander!