I agree with more Aliens and with thinking outside the box. One thing I would add, is that thinking outside the box shouldn't just necessarily mean putting unexpected people in familiar positions. It could also mean showing different positions entirely. There's no particular reason the show would have to revolve around the bridge crew or the senior officers. Depending on the setting, there's no particular reason that there would even have to be a bridge crew, per se. There are a lot of people in starfleet - aren't the ones who aren't 'chief' this or 'head of' that occassionally interesting, as well?
Not that I'm saying they shouldn't have any senior officers as main characters, but they could easily skew the mix a little in regards to Trek tradition. Let the helmsman or the CSO or the Doctor fade more to the background and bring up someone else to take their places as a main character.