There is no right or wrong answer to this. Ask 5 Aurora players and you will get 10 different answers
Personally, I concentrate on civillian techs (construction and logistics mainly with some engine/sensor tech thrown in) as long as there is no perceived threat.
After that, I branch out to the different weapons techs.
As a tip, build a couple of Military Academies and you will soon have all the researchers you want and then some (well, not all you want, a lot of them will "only" have a 10 to 15% bonus)
Of course, there are a few essential techs:
Engines are a very important tech-line (ships, power plants, missile drives)
Active sensors are also important (sensors, missile fire controls)
after those, Research Rate (compound interest), construction and mining rate (obvious) are another few that are important. Personally, I leave about 10 to 20% of my labs allocated to research rate all the time. This gives a huge boost to research in the long run (don´t neglect the civilian economy tech, or what it´s name is, cause that huge research boost will cost you a hell of a lot of money)
After that, research whatever you feel you need