College Technology Research

Military Research
In the early game, your first priority under the Military track in the College is to research Art of War I. This boosts your starting Energy by +1 for all Heroes. That makes you more likely to be the first to cast a Spell in battle, which can be a MAJOR game changer.

Once that's done, Commander technology is going to be your ongoing priority. It increases your Leadership, which determines the number of troops that fit in your army.

Beyond those two, your exact priorities will depend on your strategy. If you focus mostly on direct damage Hero Spells, Arcana (+Hero Spell Damage) is going to be your best friend. If you rely on troops for damage output, Fortification (+troop Damage dealt, separate for each tier) will be more valuable to you.

In either case, researching Endurance (+Troop HP, separate for each tier) and Titan Body (+Defense) for all troops will be very valuable. They'll help your troops live longer, whether that's so they can deal more damage on their own, or give you more time to cast Spells.

Resources Research
When you're a small player vulnerable to attack, the MOST important research to you here will be Depot Expansion. This will increase your Depot Capacity, keeping more resources safe from plunder.

To get more out of your resource mines, the key technologies are: Wood Oil (+Wood Mine Capacity), Mining (+Ore Mine Capacity), Crystal Studies (+Crystal Mine Capacity), Sulfur Studies (+Sulfur Mine Capacity), and Total Resource Capacity (+All Mines' Capacity). Each of these will increase the max resources that can be held in any of these mines before you collect, thereby decreasing your mines' "idle" time (when they are full and stop collecting resources).

Many lords prefer to upgrade Crystal and Sulfur related capacities first, as you get a constant stream of Wood and Ore from the mines in your city. Also, Sulfur and Crystal are generally expensive than Wood and Ore (just check out the Market barter prices!)

Exactly how much to invest on this track overall will depend a lot on your play style. If you intend to get most of your resources through plunder, you will see better returns investing in Military technology for better attacks. However, the boosts here can still give you a cutting edge during Gather events, etc., and are absolutely key for players who rely on Gathering.

Development Research
Top priorities here are Medic Station and Battle Medic.

Medic Station increased your Max Wounded capacity in your Hospital. This allows you to keep more troops in your city safely, without fear they'll be Killed by an enemy attack. (When you are defending a castle, your troops always default to Wounded, but they will be Killed if your Hospital is full.)

Battle Medic increases your Wounded Ratio in battle. This means that whenever you're in a battle scenario where troops are Killed outright, a certain percentage of your Killed troops will be converted to Wounded instead. The higher ratio you have, the more troops will be converted to Wounded. (Typical scenarios where your troops default to Killed would be when you're attacking someone else; or while defending alliance buildings or fighting Crown Wars, where the base Killed:Wounded ratio for both Attacker and Defender are 50:50.)

After that, your next priority should be Physique, which helps you recover Stamina faster. The more Stamina you can use per day, the more monsters you can attack, and the faster you can Level Up your Heroes.

The remaining research here is mostly speeding up various task times. Your priorities here will also vary based on your play style. You may want to research Sanitation (+Healing Speed) first if you are attacked frequently, for example. But you'd be more likely to prioritize Architecture (+Building Speed) first if you Speed Up buildings frequently, and want to save Gem Costs on Speed Up time.