Welcome to Hydaelyn!

As a rule of thumb, anything you need to know should be covered in-game. Further details (such as most information in the Encyclopedia Eorzea a.k.a. Lore Book) are nice to have and can expand your understanding, but aren't necessary to fully enjoy the story. (I don't have one myself.)

Just get into it and if you have any questions don't be afraid to ask - just beware of bias, as a lot of things are open to interpretation.
Most (in)famously Garlemald, and if you happen across a heated debate on the issue my advice is thus: