Since T3 isn't very faithful to T1 and T2, and comes off as being completely ridiculous at times, I'd say definitely not T3.
Although I enjoyed the Stirling T2 series I'd have to say I wouldn't take it as canon either. I think I recall hearing somewhere that Cameron enjoyed the series, but I'd take that with a grain of salt. The series is definitely well written, and is more respectful of T1 and 2, but there're a few things that just don't fit in my opinion. I did like that the first two books are pre-Judgment Day, and the antagonist is a human with enhancements implanted by Skynet. I guess they were going with that idea for the hybrids in Salvation, but here it's pulled off really well.
There's also the New John Connor Chronicles. I still look at it from a "What If...?" standpoint though, because it deals with three timelines.
John's World: Picks up immediately after the events of T2 with John and Sarah escaping the steel mill and hiding out in South America. Judgment Day doesn't happen.
Skynet's World: Picks up at the Salceda's camp. In the movie she had that nuke nightmare which makes her abandon their original plan of arming themselves, heading south and waiting Judgment Day out. Instead she attempts to change the future by killing Dyson. In this timeline she doesn't have that dream, they stick with that plan and Judgment Day happens as predicted.
Jade's World: In this timeline T2 happens, and Judgment Day is only postponed until the 2020s. By this time technology is far more advanced, and humans can "upgrade" themselves. Similar to Ghost in the Shell. But since humans have such advanced tech Skynet is just that much stronger in this timeline.
There's jumping between timelines, and it get's really confusing by the second book. Definitely interesting, but again, I wouldn't say it's canon at all.
To me, canon is what we saw on film in T1 and T2. If you want to go a step further, I'd also say some parts of the Randall Frakes T2 novelization are canon as well (aside from the obvious amendments like Terminator being lowered into the steel instead of just jumping in in the book).The book was written from an earlier version of the script with William Wisher's supervision, so it's as official as you're gonna get. It includes the read/write chip swap scene as well as several other scenes that were cut for pacing/budget concerns, but still fit perfectly into canon and expand on the mythos. The extended future war scene, which Cameron intended to be in the movie, but cut due to budget/time constraints, is still present as well.