Terminator: The Sarah Connor Chronicles

Optional, and the one skippable entry here worth actively recommending. It picks up a few years after Judgment Day, ignores Rise of the Machines entirely, and runs on its own branch for thirty-one episodes across two seasons.

Television suits this material better than the films admit. A two-hour chase has to keep moving; a season can sit still and ask what living under a known date of death does to a mother and a teenage boy. Lena Headey plays Sarah with none of Hamilton's physical ferocity and a great deal more exhaustion, and the show is unusually interested in the cost of her certainty, including the possibility that she is wrong. Summer Glau's Cameron, a machine sent back to protect John and pass as a girl his age, is the best non-Schwarzenegger terminator the franchise has produced.

It is also the only part of the series that takes an interest in the machines as something other than weapons. A subplot about an AI being raised deliberately, in a basement, by a man teaching it chess, is better than anything in three of the films.

The caveat is real and you should know it going in: it was cancelled on a cliffhanger. The last episode sends a character into the future and ends. There is no resolution and there never will be, and if unfinished stories irritate you, do not start.