As far as actual lore provided goes? Id say its a tie between SCH, SMN, MNK and AST. WHM had stuff but a lot of the things we saw were rather vague in terms of detail. WAR, NIN, DRG, BLM, DRK and BRD got into details on their particular arts but were mostly personal stories. PLD was just confusing and seemed kind of pointless.

SCH gave us a lot of insight into the Nymians. Most of our understanding of them and what happened with them and the Tonberries comes from that quest. It is one of our most detailed sources of info on the War of the Magi.

SMN touches on the Allag but it also goes into the nature of primals as well as being really our only window into the nature of the lesser Ascians, something the MSQ never deals with.

MNK not only had a story discussing the nature of MNK techniques and the way Aether travels through the body but it also had Eric's rather interesting lectures on history. A lot of what we know of the Autumn war and Ala Mhigo comes from the MNK quests and Eric's lessons.

AST introduced the form and function of celestial bodies and their influence on the Aether, and Fate as well as showing us not only a window on Ishgardian politics but Sharlayan politics. Special mention to the Pole star which is only visible at the moment of death and judging by what we know of the other six consolations and Eorzean metaphysics seems to tie to either Hydaelyn or Zodiark or both.