When I was in Zürich, I was considering a GA pass for travel pretty much all over Switzerland.
Now I'll be living in Genéve, and a GA pass doesn't seem nearly as useful, as most destinations within about 250km are in France, and the card is not valid there.

What sort of rail pass would you recommend?
A local Geneva pass + halbtax card + some sort of a French rail pass?

I saw something about a Rail Plus upgrade that would get an additional 25% off (in addition to the 50% off from the half tax).
Does that bring it up to 75% off, or is it 25% off the remaining 50% off (ie 62.5% off)?

Is there some sort of pass that applies to Geneva+ the surrounding French area (like Annemasse?)

Hi, no idea about the French region and their passes, so, sorry about not being able to chip in much. GA is great, though, if you want to explore CH, I work in 3 cities so it is so worth it.

The transportation in France is more difficult for me to navigate, even though I live a few kms from the French border, still venture out a lot more inland CH, just to be able to see the country. The occasional trip to France is ok without some special pass for me. Car has proven a lot more useful in France.

The Genevan transport system is called Unireso (French only I'm afraid). The linked page gives details of the tarifs. You need to choose between just the canton of Geneva or the extended network, which covers neighbouring Vaud and neighbouring France (including Annemasse, Pays de Gex).