The Advancement Tree should be the first place you focus your attention. Once you hit Academy 25 you can take your Military Tree up far enough to get your 5th March Slot but then you should immediately return to the Advancement Tree. The Technologies (Techs) in this tree are focused around things that will help you in the long run, saving you thousands of days worth of speedups and helping you accumulate resources much faster!
Construction, Advanced Construction, and Super Construction:
All three speed up your construction speed, vastly reducing the amount of time it takes to upgrade buildings in your city. I'm talking days or weeks off of medium length builds and entire months off of the later game builds like Keep 32-35. You want to keep these Techs maxed to whatever your Academy level will allow to gain the most benefit possible from them.
Typography and Super Typography:
The Research version of the Construction Techs. These reduce the amount of time your Techs take to finish. Again this bonus is huge and you should keep these maxed as well. After upgrading your Academy you should immediately upgrade these two Techs before moving on to the Construction techs so that they benefit from the reduced research time.
While increasing the amount of gold you get from Levying doesn't seem like that big of a deal, it is. Over the course of months, having this maxed will net you hundreds of millions more in gold than if you had ignored it.
Resource Gathering and Production Speed (Lumbering, Mining, Logging, Ect):
These Techs will help you accumulate resources faster by increasing the hourly output of your resource fields and increasing the rate at which your troops gather from tiles. While these Techs provide a massive boost in the long run, it's not essential to worry about them too much until after you have completed a lot of the combat based Techs. When you're in doubt of what Tech to research next, or there's not much left of importance to do at your current Academy level, you should slap through a couple of these to help yourself out.
Gathering March Speed:
Speeding up your march speed to tiles is bottom of the priority list.
Carriage Wheel and Advanced Logistics:
Increasing your troops load will allow you to carry more resources back from tile or battle. While helpful, its not a top priority for sure.
Gems Gathering and Advanced Silo:
There's not much to say here. If you keep your food in boxes until you need it and send any extra you get to the Alliance Warehouse, you really don't need to protect more food from being eaten until later game.
Gems Gathering is also not a thing you need to worry about if you can drop $5 every now and then or participate in every available event that rewards gems.