Yes! New series. Since it'll probably be done by Bryan Fuller of the awesome (and cancelled) Wonderfalls and Pushing Daisies, who's been capaigning to do a new series anyway, I'd vote for Lee Pace as the star. Those two seem to like working together anyway; besides Pace actually looks like a 1960's movie star.
In order to keep the new show from stepping on the toes of the JJ Abrams movies, I would keep it in the Star Trek universe but NOT on a Star Fleet ship. I would totally rip off Firefly and set it on a pirate/smuggling ship operating on the outskirts of the Federation. Maybe a stolen Romulan Warbird? (since I like that design) with a cloaking device and a largely ex-starfleet crew.
The main cast would be former officers who were kicked out Starfleet for various reasons (that would be explored or hinted at week-to-week) who now exploit their knowledge of Federation patrols and protocols to evade capture, and pull off daring heists.
They would be pursued by a Federation starship twice the size of the NuEnterprise captained by a stick in the mud intellectual, much like Picard only less experienced or charaismatic and more way more pedantic and bureaucratic. The Captain of the pirate ship would be a lot like Kirk, only less ethical and more of a bitter anti-hero (kinda like Mal from Firefly). As they play this cat and mouse game through the galaxy the human crew of the pirate ship unconsciously bring their 23rd century Federation/Rodenberry idealism to their shady business deals and criminal enterprises.
As you can see, I've thought a lot about this. I think the main inspiriation came from the one-two punch of Star Trek III and The Voyage Home. As a kid watchiong those movies, I would have been more than happy if the crew of the enterprise stayed on The Bounty continued being chased by The Exelsior (or whatever) in at least one more movie.