Time travel can be confusing. Every time someone steps into a time machine, it changes everything. However, that can be convenient for writers piecing together new movies -it explains every continuity goof and every great new idea that would be hard to explain otherwise. io9 lays out ten different timelines that work in one part or another of the Terminator movie series (and TV show).
I’ve mulled it over some more, and I still believe there has to be a timeline where someone other than Kyle Reese is John Connor’s father. When The Terminator was a standalone movie, you could read it either way. Either there’s a circular causality, where Kyle is “always” John Connor’s father, or Kyle’s time travel creates a new branch. But Terminator 2 pretty much establishes that time travel always creates new branches, because there’s no fate but what we make. And the Connors, with their friendly T-800, are able to stop or at least delay Skynet. But of course, your mileage, even backwards and forwards through time, may vary.
Whether they make complete sense or not, reading these may help prepare you for Terminator Salvation.