Martial Warfare; Arcane Sudies; Fiscal Knowledge(Scholarly); Religion, Population Growth(housing, farming, city works), Commerce Based economy(and trade), Naval Warfare(and possibly aerial as well), and last but not least- Beastial Mastery (of the ways of beasts and how to raise/recruit them)
in this case there would be 8 basic technological groupings, 4 economical and 4 militaristic. This is an argument in favor of focus-based research. For while I can competently prioritize tech progression in a 4x fantasy game, I believe that focus allows for more RP settings, and that the type of tech you decide to delve into (focus) would be more closely because you want the benefits that lie theirin, rather than simply filling out prerequisites for some grande super strategy ... for instance in FFH, picking the Industry civ (one of the dwarves) and slingshotting your way to summon angels while most people only have basic axemen, and if they are lucky-catapults.
Going for Mass Warfare? alternate between Martial Warfare and Population Growth. Elite soldier caste? Fiscal Knowledge and Martial Warfare. Zealots and Jihad/Crusade? Pop growth and Religion. Passive Philosophers? Fiscal Knowledge and Religion. Super-Magic? Arcane Studies and Fiscal Knowledge. Battle-mages/ buffs for army? Arcane studies and Martial Warfare.
And ... if you are more focusing on recruiting Worldly and Other Worldly beasts and their followers, then Beastial Mastery is the way to go.
I will go into several Beastial Mastery archetypes, as Beasts are important to me.
Compliment your army with Common Beasts? Martial Warfare and Beastial Mastery (bear riders, griffon riders, CAVALRY!!)
Search the plane for ethereal Beasts of power (like archangels)? Arcane Studies and Beastial Mastery
Worship beasts for high morale bonuses? and bonuses for the beasts themselves? Religion and Bestial Mastery
Wish to communicate and command beasts of the high seas? Naval Warfare and Bestial Mastery
Wish to gain the ultimate techniques in raising a dragon, to Gain the Respect and Full command of the Most powerful beasts in existence? Fiscal Knowledge and Bestial Mastery.
Fiscal Knowledge of course will of course hasten and compliment your ability to reach the high tiers of the other forms of research, although I think within Fiscal itself, there should be alternate and improved strategies and techniques found with logic and reasoning (Fiscal) that opens up new pathways in your chosen element (say population growth).
For instance, in Fiscal Knowledge could be Architecture and city planning, which can greatly improve the efficiency of your cities with new improvements to building plans, ect. Could allow for more densely populated cities, which leads to less need for land. Improvements found in a field gained from repitition/ad nauseam should be found within the field, but milestones in cognitive innovation .... I believe should only be unlocked by delving into Fiscal Knowledge.
Likewise, my system does not contain a Field of research devoted to Industry or production. I believe that industrial techniques for each (wether alchemist labs (magic), blacksmiths (martial), socratic schools (fiscal), market places (commerce), dockyards (naval), Hatchery/Nursery (beastial), monastary (religion), granary silo (pop growth) ) should develop within their own field. Battlefield surgeons, and basic non-magical medicine/sanitation, should arise from the bedding of Fiscal Knowledge with Population Growth.
In essense, the ability of constructing buildings faster would be within the City Planning section of the Pop Growth research field, while the ability to contruct units faster (especially massive numbered units faster) would be in the MOBS section of Pop Growth. However skills in making weapons/armor faster would be under Martial, and making boats faster would be under naval.
Arcane Studies linked with Fiscal Knowledge could lead to greater steps made in meditation and Socratic thought, leading to faster Spell researach times.
Steps in Bestial Mastery will link to more varied and advanced usage of beasts, including unlocking new beasts you can interact with. Linking with Religion will open options for cult-like worship of certain beasts, granting specific morale bonuses to both beast and men, while linking with Fiscal Knowledge open new tactics with beasts (ride an eagle? use them to paradrop troops mid-battlefield? teach a kraken to form a naval blockade?) and open up greater respect from the higher intelligence beasts ... eventually unlocking ways with which you could raise your own dragon. And then you would have to find and capture the egg, yadda yadda.