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Hey there, and welcome aboard!
About as much as I can suggest for lore sources that are easily accessible is probably the wiki, which has at least some basic information:
http://ffxiv.consolegameswiki.com/wiki/FF14_Wiki
Beyond that, I think the best way to get familiar with it all is just to play through the game. This is one of those games where quest text is often story-driven, especially in the case of your class quests as well as the main storyline quest. The storylines are actually anywhere from fairly decent to completely awesome, so they're certainly worth the time in doing!
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About as much as I can suggest for lore sources that are easily accessible is probably the wiki, which has at least some basic information:
http://ffxiv.consolegameswiki.com/wiki/FF14_Wiki
Beyond that, I think the best way to get familiar with it all is just to play through the game. This is one of those games where quest text is often story-driven, especially in the case of your class quests as well as the main storyline quest. The storylines are actually anywhere from fairly decent to completely awesome, so they're certainly worth the time in doing!