As TEC, the very first things you want to research are Ice/Volcanic colonization ( for my style at least ). Which one you choose first depends on what type of planets are closest. Don't waste time or resources on a planet type that you don't have nearby ( use your scouts ). I don't even make a military lab until after I have two civic labs. You want to expand as fast as possible, that means being able to colonize. Then can come Psidar, trade ports, and mining buffs. Anything other then colonizing, Psidar, and trade ports is frosting for me on the civics tree. End game, when you have credits to burn, it's nice to have insurgency and max'd mining buffs ( sell that stuff for $$$ ). Trade buffs are nice too.
Next up, is military labs. Depending on the area and map, I make my choices on what I am going for military wise. I usually get some armor/shield/repair techs while working towards 5 labs and Kodiaks, not forgetting to pick up LRM's on the way.
That should do for a start, at least against the AI. People, thats depends on who you're playing and thier style.
If you love static defenses, you can get fancy with repair bays, hangers, and and upgrades for turrets. Some people go nuts for LRM upgrades which is nice, since it puts you closer to a novalith. Others get every HC they can. More go for weapon/armor/shield upgrades. After a good base, it starts to depend on your style.