I already finished Black Eagles and Blue Lions and I'm midway through Golden Deer. With the amount of info I have now of the game, If I could go back in time I would choose the following order:
Golden Deer > Black Eagles > Blue Lions > Church
The only problem with this order is that the Flame Emperor reveal comes out of nowhere in Golden Deer, there's at least certain amount of foreshadowing in the other routes but aside from that, this would have been my ideal order