Voted. I'll be back when I have more time to expound on which one and what I'd do with it.
OK, I'm back. I voted for Enterprise. Aside from loving the show, I really liked the idea of a prequel... Trouble is, I expected something more along the lines of Star Trek: The Right Stuff.
I would have set it in the last decade of the 21st century. Earth is still a post-war mess but humanity is making progress toward unity and global peace.
The NX-01 crew represents several nations, a group of brash, cocky astronauts. The ship has technical glitches, there are injuries and death, and lots of misunderstandings and mistakes based on human-centric thinking. Occasional cases of xenophobia when they come across a particularly alien alien. There would be subtle evidence that the crew is engaging in fraternization.
While I'm OK with the idea of a Vulcan "babysitter" being shoved down the crew's collective throat (as long as the crew is resentful and suspicious for more than a few episodes in season 1

), I would have had a human doctor with some background in interspecies medical training, but not an alien superdoctor who can cure and fix anything. As a result, crew members and guest aliens will lose body parts, get seriously ill or injured and on occasion die! It's supposed to be DANGEROUS out there!
Enterprise would have to return to Earth once in a while to replace maimed and dead crew members, make repairs and pick up supplies and equipment, so some episodes would be set on Earth where we'd get the chance to explore familial relationships and Earth-based friendships along with Star Fleet and civilian life on Earth in the late 21st C.
There would be no instantaneous communication with SF (I don't care how many relay satellites they drop). Laser-based hand weapons; no stun setting, tho' the shooter would have the option of causing injury as opposed to "shoot to kill." No transporter. 100 percent reliance on shuttlepods.
The ship would be a larger version of Cochrane's ship. Crew quarters would be even smaller than we saw on the show. The captain would not have a ready room. If you wanted to privacy, you'd go to your quarters (and hang a towel on the door to keep your roommates out

).
T'Pol would very gradually become friends with two or three members of the crew, but most would remain wary and suspicious.
Main cast:
Capt. Jonathan Archer: Doesn't like Vulcans. He resents their interference in Earth's affairs (not to mention they tried to block his appointment as captain of Enterprise).
T'Pol: Vulcan "adviser." Actually, she's reporting back to her superiors to make a case to remove Archer, who they consider to be reckless.
Commander Charles "Trip" Tucker III: Chief engineer. Archer's best friend. The only member of the crew who gets away with challenging the captain's preconceptions. He's the first to try to befriend T'Pol. It doesn't go well.
Lt. Malcolm Reed: Tactical officer. He also has a covert assignment, unknown to Archer. Section 31, his first job with SF, has evidence of incursions into the region that could be a precursor to invasion. Reed's instructions are to get every scrap of information on every species Enterprise comes across. In some instances, that will create friction during some of the ship's first contacts.
Ensign Hoshi Reed: Malcolm's wife. As a civilian, she was an interpreter for the new United Nations. She joined SF after learning Reed was in line for assignment to the NX-01. She has a gift for learning languages and is assigned as linquist and protocol officer. Her background leaves her ill-prepared for encounters with aliens and the dangers that lie ahead.
Travis "Boomer" Mayweather: Security chief. Ship's practical joker (only in my version, where we show, rather than tell, we'll actually see the pranks. Malcolm will be his favorite target, much to Hoshi's bemusement).
Dr. John Phlox: Has two years' experience in the Interspecies Medical Exchange. As a result, unlike much of the crew, he's very comfortable with non-terrestrials.
Lt. Elizabeth Cutler: Physician's assistant. She will often accompany landing parties during missions away from the ship to provide medical care as needed.