What's the most important thing to research?

[Lemmy]

i usually go for physics and then phased energy weapons, ship construction and shields

The phased energy weapons are one of the more expensive weapons but they are still powerfull later on in the game, i haven't researched anything stronger yet ( (damage/size)/fire rate, that's what i use to define strong ), troops are also good, that you can capture there planets and if they breath a different atmosphere you can also colonize more planets,
military science/ship capture is also very useful, especially if you capture a different colony ship type, or a larger ship and analyze them at your shipyards.