Agree with
@s0nny80y I'm not usually a warmonger, meaning conquest victory, so I tend to pursue Harmony or Supremacy victory conditions. Since NSA can found Deepcastle as an aquatic city, that could mean some complications for pursuing Supremacy. I found out the hard way that if you build the gate on a water hex, all the land units you want to send through to conquer Earth are *embarked* when they go through. That means much less combat strength than their land versions and you have to send a lot more of them. Make sure that Deepcastle (or another strong production city) is located near enough to land, so that the gate can be built on land, to send through full-strength units.
It helps to look at your available resources, too. If you have Firaxite nearby, then going for Robotics to mine it will also earn Supremacy affinity points. If you have Xenomass nearby, then you may want to consider going for Harmony. I always research each of the techs to build improvements on Geothermal, Firaxite, Xenomass, and Floatstone. That tends to get me a few affinity levels in each of them. As I explore the map, I decide which victory condition would work best. The affinity quests and Progenitor Ruins help accelerate leveling up affinities.
I have not tried Purity with NSA. I believe that the Earth colonists have to end in settlements on land, rather than aquatic, which might be a challenge if I've built a bunch of aquatic cities to establish my colony.
Note that the tech tree has nodes and leaves. The node tech gives some affinity points, but the leaf tech under it gives *more* affinity points. Consider your tech order to build up those points, trying to get to level 15 as you learn the last tech to enable building the gate or Mind Flower.