How do I approach the tech web?

The new tech web is a little harder to get used to, but it opens up the tech a lot more and makes more sense given that you're not having to, say, invent counting before you can open a bank.

Typically, while you're learning your way around the web, there are three goals: In the short-term, you want things that will either immediately benefit you or raise your science production. In the mid-term, you're looking for your affinity of choice and its thematic technologies. In the long-term, you want your affinity's really big guns, like Harmony's "heal in miasma instead of taking damage".

Pay attention to your science output and look at how many turns particular techs will take to research, and then decide on your priorities. Remember that the further a technology is from center, the more it will cost. After slogging through a long, slow upgrade, snag a handful of cheap ones from around the center.

The biggest thing is really just choosing an affinity. Then you can just work on paths to that affinity's experience points on the web until you get sidetracked by a must-have upgrade.

While each direction on the web has a certain general feel, I don't think any major generalizations can be made. No up=science, down=military type categories, although I could easily be wrong about that (it's been a while since I played).