Dealing with culture is fairly simple.  Building 1 culture buildings of your own can easily put out enough culture to defend against 2-3 enemy culture buildings(culture is a lot stronger per structures on defense then one offense).  This is one of the chief reasons culture offense is considered inefficient- actually pushing through enemy culture is very cost ineffective as you need to spend far more then the defender, and they can't negate your efforts by turning that economic edge into a superior fleet that culture will do nothing to stop.

 Additionally, your capitalships push back enemy culture when in friendly or neutral gravity wells(they push back culture most effectively when stationed in friendly gravity wells).  So an easy way to buy time to put up a defensive culture building is to station 1-2 capitalships in the well that is being culture-pushed.

Once you get used to usign these tactics you'll  see why most multiplayer players believe culture-offense to be a trash strategy- it takes a long time to flip a planet and the counters are extremely effective.

As for general techs: for most of the game you want to go very light on techs in general.  Generally in the early through midgame you'll only really want to grab prototype techs(anything that unlocks an important ship, structure, or ship/structure abilities) and perhaps some early eco techs like modular infrastructure or expediated permits as needed.

If you are going pure eco early and aren't under much pressure you can also rush for Truce Among Rogues for massive expansion rate.

That said, most players typically go rather light on thing slike weapons upgrades for most of the game- Until the super later game it's generally a better idea to focus on increasing the size of your fleet rather then upgrading the stats of the ships you already have.  or conversely if you're going heavy Eco you're usually better off building more trading posts for much of the game then you are actually purchasing expensive upgrades.   If you get to the Very end of the civic tree, Pervasive Economy is a tremendously powerful tech, and since the TEC is all about winning a war of attrition with their superior economy in longer games you'll likely want to eventually grab some of their trade income upgrades.

Of course in long games there comes a time when your economy/fleet is large enough that it's more efficient to start actually upgrading, but in all honesty many games are decided long before that point.  In truth while theres some degree of learning what to tech against a given enemy in play, most of learning to etch properly comes down t oelarning how to be frugal and makes do with only the couple of techs you really need so that most of your money can go to building tradeports or improving your fleet size.

By the way in which tree is the culture building and what's it called?

As the TEC rebels (and against the AI) your big military advantages mid to late game are the Ragnarov titan, excellent repair, and Missile Barrage on the Marza (probably in that order).

Ragnarov - Snipe is a really good ability but the key here is Explosive Shot + Overcharge.  You need to get the Ragnarov to level 7 to fully take advantage of this (4 levels of Explosive Shot + 1 level of Overcharge) but when you get it, you can kill large numbers of enemy frigate with a single shot.  The key here is that Overcharge doubles the damage and doubles the AOE range over which it does this damage.

Repair - TEC in general have the best repair in the game.   The key combination is Repair Platforms + Hoshikos + Docking Booms on the starbase.  Together they will repair 75 hull points / sec with the bonus that Docking Boom also recharge the antimatter on the Repair Platforms and the Hoshikos so that they never run out of antimatter.  This gives you a huge bonus when on the defense / fighting around a starbase.

Missile Barrage - This is the strongest AOE damage ability of any capital ship in the game.  You have to be careful when you use it because the AI will interrupt it, but it can be used to severely damage enemy fleets.