I haven't gotten around to seeing the third and fourth films, nor the series, but I always thought of the original movie as presenting a self-contained predestined time-loop. It is not logical, and I would never expect such a thing to exist in real life even if someone ever did invent a time-machine, but for dramatic purposes I like the idea that Kyle Reese was always going to be John's father, and that Sarah was always going to train her son to fight the machines.
Although T2 was in some ways more exciting and better than the original, it always disappointed me they ended the film by seemingly preventing the future war. It undid the beautiful "A storm's coming" ending of the first movie.