I think a CW series would be fun. I've never had a problem with hot chicks sleeping around and with Kirk and Riker's reputations, neither has Trek. It would open up a huge new audience, although many in the current audience will say it's not Star Trek. Personally, I've always considered Trek to be the universe not just the specific shows or characters. I think there is plenty of room for a CW show in that universe.
Another idea I wanted to throw out there. I think a miniseries would be a great idea to. If anyone has seen HBO's John Adams with Paul Giamatti. It was 8 or 9 episodes that followed his life from just before the Boston Tea Party to his death. I've thought that something similar could be pretty cool for ST. Maybe follow the life of Worf. Especially set in the new timeline, we can see how his life might be different. I could see the finale with him walking onto the bridge of the Enterprise for the first time or something.
But as someone mentioned before, Star Trek sets aren't cheap. I'm sure they can reuse the bridge and wardrobe from the JJ films to begin and offset some of those costs(obviously, not for the Worf Saga) but maybe rather than a straight miniseries, they could do an Anthology series like American Horror Story
. I think they use the same cast to play different characters every year, but ST could just have different crews and casts for each year. They could even set it as all happening at the same time. Each season is the year 2350 but from the POV of different people and ships.