Controversial opinion, but I don't think the future setting is good enough tor really explore. Terminator is essentially a time travel story, and a focus on the future setting takes away from that. One of the things I loved about Sarah Connor Chronicles is that it expanded the use of time travel beyond the whole kill/save John Connor dynamic. Terminators and Resistance members were coming back to essentially prep for the future war, setting up supplies while also attempting to change/assure the future. It was also good to see how going back to where life was better affected the humans coming back.
I also loved how it picked up on a few small tidbits from 2 and 3, and was starting to expand on it. Why was Skynet trying to prevent its creations from gaining sentience and why the T-X even existed. Connor was not likely commandeering enough Terminators to require the existence of a model designed to fight other machines. In SCC, there is a breakaway, rogue group of machines, represented by a T1000 that went into the past to try to create a more humane Skynet AI. It was a fun new wrinkle in the war.
I also enjoyed the bit with a Terminator accidentally going back 90 years before the date he was going to attack his target. So, he robs banks to get capital, creates a building company, utilizing minority labor treated fairly, and builds the building with him in it where he sleeps till the time of his target.
The Terminator franchise is ripe for some great hard sci fi content. I think it could be able to be as good as the 12 Monkeys show.