There are lots of nice tech, but very early I would:
Weapons: First the second weapon, which is a huge early game buff to damage if you run AI designs, at least. Then improve the primary and secondary, and try grab star fighters quite early. Notice that tactical interceptors unlock carriers, but that is not very early. There is not so much competition in this tab. Two weapons, fighters of all kinds, point defenses, and armor when it feels cheap. Ion weapons don't hurt after a while either.
Energy and Construction: The easy way is a beeline for the Shipyard wonder in Accelerated Construction. Ignoring that, ship size is still my first, and generally of high priority. Apart from that I tend to spread wide and do level by level, but of course pick my Shield, Hyper drive, Reactor, and Engine tech.
High Tech and Industrial: First a colony tech. Then maybe another one. More colony options are better. Apart from this, maybe look for wonders early, otherwise all is nice to have. Personally I got a soft spot for long range scanners and want those early, but not early enough to not grab a ship size or two.
Research points arrive faster and faster as you grow, and the early techs are very fast to research after a while. Deconstruction of alien ships and inherited pirates helps research the early techs you don't want.
And of course notice that to reach the late techs, you sometimes have to research multiple competing techs. But it is no need to research the techs you don't plan to use unless you are actively going for the next level.