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.