Personally, I wouldn't necessarily want to see a story based on Warriors of Light, we have the game for that. Rather, I'd love to see a story based around the NPCs who were born and raised in Eorzea (I.E. none of us; personal head canon aside, our characters were all introduced as freshly arrived in Eorzea, whether they were created before or after the calamity), with slice of life episodes and such. Maybe a "prequel" series that shows the efforts of the people of Limsa Lominsa, Ul'dah, and Gridania establishing their cities as we know them today. Conflict between them and the indigenous beast tribes, politics, a semi-origin story of the leaders of the city-states becoming who they are now, occasional mention of news of the empire's exploits, maybe side stories depicting their invasion of Doma and Ala Mhigo, etc.

Given how fleshed out they got with the lore book, there's a ton of different places along the timeline they could base an anime series in.