As stated in my Where to Start guide, the Military Tree is going to be a major priority after your Advancement Tree even before the Defense Tree. Here you will find the most important Techs when it comes to your troop stats. These Techs lay the basis for your overall buffs in the game. You will also find Techs for March Size, March Speed, and Troop Training Techs. You will find that very few of these Techs are Non-Essential.
All of the Troop Stat Buffs:
These Techs are absolutely vital to your gameplay. Without them, your troops are 100% useless. You should start by doing all the Straight Points Buffs for all troop types just to get them out of the way then move on to the Percentage Buffs. When doing the Percentage Buffs its ok to focus on your main Troop Type at first, but eventually you will want to return and finish them all.
Formation, Advanced Dispatch, Super Advanced Dispatch:
By Keep 25 you will add 3 march slots just from this Tech Tree. Get these sorted out right away as you will be able to join more rallies and send out more marches to tiles while offline.
Coordination, Adv Coordination, Super Coordination, Supreme Coordination:
Troop Moral, Troop Defense, Super Troop Moral, Super Troop Defense:
These Techs add to your troops Attack and Defense stats only when attacking, so if you are going to focus your Defense and not worry so much about attacking people then these are ok to put on the back burner for now. Otherwise, you need to get these finished pronto to give you an extra boost when attacking people.
Tracing and Advanced Compass:
Increasing your March Speed is a huge quality of life improvement for your gameplay. Being able to join more rallies because your troops come back faster means your growth with speed up as well.
Conscription, Advanced Conscription, Super Conscription:
You probably don't want to focus too much on building a lot of troops until at least T12s so you can worry about Training Batch Size and Training Speed until then. This coupled with the fact that you will rarely if ever run out of Troop Training Speedups makes these rather low priority.
There are much faster ways of leveling your generals. Power level on a Subordinate City or just throw the General you want to Level into a Subordinate City during Battlefield will be magnitudes faster and negate pretty much any bonus you really get from this Tech.