I'd first try to pitch Paramount & UPN a sci-fi series that wasn't set in the Star Trek universe. I would push something with the same sense of exploration, but with entirely new set of aliens, ships, etc -- something with a decided 'transhumanist' approach.
Barring that, I'd probably do a series set post the other series. New story editor, instead of Braga, and a small clique of good writers who would work together to keep a tight continuity. I'd try to explore more of the Federation itself -- what worlds haven't we seen? What creatures could be explored? I'd try to lose the purely episodic format in favor of multi-episode stories, so we can get a better picture of worlds that are explored, give grander-scale plots, etc...
New actors and maybe one 'name'. I'd set it on a ship -- probably an Akira.
No holograms, thank you very much. I would explore androids as an up & coming 'race' that is at once advantageous & really scary for the organics...strong, smarter, faster, and highly adaptable, these new generation androids would be more lifelike. And the element of a possible enemy inside the ranks would be more interesting than another failed Borg invasion.
More CGI-based non-humanoid aliens.
A tighter reliance on real science over the over-the-top technobabble.
"War is an ugly thing but not the ugliest of things; the decayed and degraded state of moral and patriotic feelings which thinks that nothing is worth war is much worse. A man who has nothing for which he is willing to fight, nothing which is more important than his own personal safety, is a miserable creature and has no chance of being free unless made and kept so by the exertions of better men than himself."
John Stuart Mill