Well I think in some ways, using the 'nuTrek'-verse in any kind of animated or live action tv show might be a bit... rough. Considering that so far we've only had one and soon two live action movies in this universe. You don't want people bitching that 'the goddamn cartooon's canon was already violated by the movie canon" or vice versa.
I think really, the easiest thing would be to set it in the Trek universe we've known and loved, maybe still go back to Kirk and Spock days, but Shatner/Nimoy Kirk and Spock. Or shoot ahead to Post-Nemesis - there's still a lot of ground to cover between the end of Nemesis and nuTrek. And if you make it animated, then you don't need to worry about the expense of a large cast or all new sets - I for one would love to see some indepth look at the Romulans and their culture, a little more on some of the more nebulous races like the Breen.
I wouldn't really want it on something like Showtime - since really Showtime doesn't do animation anymore, neither does HBO. FX probably would be the most logical choice really - it's still cable but they've got Archer and if it's a bit more 'adult', you could even argue with a show like Sons of Anarchy, they can get away with a lot too. Market it the same way they do Archer, which is hardly a kid's show. Get some good animation teams on it - doesn't have to be CGI, except maybe for the ship battles - hire a decent Anime company to do it. Certainly not Madhouse. Tell them not to do the typical "Anime' tropes of big robots, big hair, have everything set in Japan... just tell a good, stylish, well done Star Trek story. I'm sure someone could do it, reasonably, get good VA talent. Hell, it's voice over, they could afford Patrick Stewart and Brent Spiner here and there - if those two can do silly stuff like Family Guy, I'm sure they can't be all that expensive to hire back for Trek.
Beauty of it is, they don't even really need to go anywhere, they could literally phone it in. Isn't technology grand!