The thing about Terminator as a franchise is that even though T1 and T2 directly connected with each other, the other films don't really connect to any of the characters or key plot points of any other film. I really think they are best viewed as standalone films that share similar themes and elements. Even the character of John Conner is wildly different depending on which film you watch. Their oscillation overthruster must be creating faulty exchanges of virtual photons.
As much as I loved T1 and T2, for me the crowning achievement of the franchise is the two seasons of the Terminator TV show, the Sarah Conner Chronicles. Plenty of mystery, characters you love to hate, characters you hate to love. Twists and turns as you try to decipher just how many factions are in play, where they all come from, and what they all want. Even the cliffhanger ending of the second season is retrospectively a perfect way to leave the story, not at all neat and tidy and kindling that dread of the inevitability of Judgement Day afresh. It's a horror story ending of the futility of hope that combines with a Lovecraft-esque crushing of John Conner's spirit when his role in the story - preeminent up to this point - is reduced to insignificance.
But the moment that sticks with me is one episode in the middle of season 2, John and his uncle Derek Reese spend the episode saving one particular boy because his role in the future is crucial. When John finally asks Reese what this boy does in the future Reese replies, "He dies for you, John. We all die for you." Chills.