The only way you could pull of one or two movies (like they did with Battlestar Galactica) is to use establised characters.
I don't see why that would be true at all. Star Trek
is the known brand name to use as the main draw, and unless the show is animated, they can't make use of the well-known names of Kirk and Spock, so they may as well just invent new characters.
It's possible that characters from the other series could be recast (most of the actors being simply too old by now to build a new series around) but other than the TOS characters and Data, they really aren't iconic in their own right, as a separate thing from the actors who played them. I could see Alan Tudyk as Data. I really can't think of another non-TOS character who could be recast and still be a draw.