[StevenS]

I'm aware that they already did the time travel thing, but they did a piss poor job of it. Why not send back the badass chick from the second movie. Hell, why not just kill his grandfather or something?

I bet they're the reason dinosaurs became extinct.

The Terminators didn't invent Time Travel, humans did. They have to infiltrate the resistance's base in order to use their machine, so it's not like they can send an infinite amount of them back through time. You also have to keep in mind that these killers are machines, and therefore only use a linear thought process and do not think like humans. If you remember from the movies, the Terminators are "programmed," and therefore are set out to do a singular mission. I would imagine after "Judgement Day," a lot of history was destroyed due to nuclear fallout, so I can't imagine there would be a plethora of archived information on Connor's genealogy.