How Much Should I Upgrade Geos?

It really depends where you are as a player.

For brand new / very low gp players I'm going to buck the conventional wisdom (which is largely outdated) and say Geos can be safely ignored until much later. They're kind of a trap faction at this point. Sure there's some things they do quite well but there's just too much other better stuff you can be focusing on first and they get countered too easily. Their fleet is fine but there are other approaches you can take early-mid game for fleets and do just as well. You're in a 6+ year hole in terms of resources so you really have to take a brutally frugal approach in order to get up and running.

If you're past the very early game and have already somewhat invested in them already, then that changes things. I'd still say don't take them any higher than just good enough to beat the Wat mission, and then leave them in the dust. It can be done pretty consistently at about 80k or just under / ie most of them at purple gear with perhaps a couple at g12.