What Terminator needs for a successful reboot, in my opinion, is not necessarily a remake but re-imagining of the first movie.
A killing machine from the future that will stop at nothing until it's target is terminated.
Remember Kyle's speech to Sarah in the first film about what the Terminator is? It's friggin' frightening as all hell!
Brand new characters, new designs, just keep the concept. Find a way to make the simple thrill of the chase compelling with high stakes, characters you can care about, no Arnold, no Connors. And it should be an unsettling 2 hour ride while you go through the experience of being hunted with those new characters.
Not a fun trip through nostalgia land.
Edit: Maybe even have James Cameron write it, and hand pick a director, BOOM! Or go with all new blood, who won't be afraid to shake it up.