If I had free reign of characters but had to stick to the Earth Starfleet/Pre-UFP setting then I might go for something along these lines:
Captain Indira Sholi: Martian-born human woman of Indian-British origin, in her mid-late 40s. Among the first class of the newly formed "Starfleet", she graduated in the top 5% and has made being in space her life. Despite the initial intent of Starfleet being primarily to defend Earth-held space, as she rose through the ranks and gained more prestige and sway (thanks to her sharp tactical mind as well as her ability to foster positive relations with other species) she has taken a vocal stance for Starfleet to be more, for humanity to truly take its place as an interstellar species and get out there and explore, instead of just dipping their tow in to test the waters. Due to the persistence of Sholi and others, Starfleet Command opted to expand their horizons, and when the NX-01 was commissioned her name was at the top of the list for candidates to lead the mission. She believes in leading from the forefront, almost always going on landing parties (especially those that involve first contacts) and embracing the role of being a trailblazer and explorer.
Commander Hunter McCain: Sholi's right-hand man and Chief of Security. The two have served together for a number of years and have a close bond, she is affectionately known as Auntie Indie to his children and his husband call her Hunter's "work-wife". Since they have been through so much, they know how one another thinks and have formed a solid and dependable team, though when she asked him to join her on the NX-01 he was hesitant as it would mean so much time away from his family, but they were the ones to persuade him to take the post, turning down a command of his own to be a part of such a monumental mission. When the excrement hits the fan he is a force to be reckoned with, but off the clock he is a warm and welcoming man who puts all at ease.
Sub-Commander T'Pol: A concession made to the Vulcan High Command by Starfleet Command was to permit them to have a representative onboard, to provide them with their knowledge and advice, as well as access to the extensive database the VHC possesses. She fills that role as well as being the ship's Navigator, making the most of Vulcan star charts and her expertise in cartography, mathematics, and astrogation. Though she may appear cold, detached and utterly logical, she has held a great fascination of humanity and all that they have accomplished is such a short space of time, having been almost at the point of decimating their world and one another.
Lt. Commander Charles Tucker III: Still in as Chief Engineering Officer. He is pretty much as he is in the show, though maybe tone done the "Southern-isms". He's a brilliant engineer, supervised the work on the NX-01, but hasn't been very far away from Earth-held space, so is keen and eager to get out and explore, as such he is sometimes a little awestruck by what he finds out there. [What can I say, the producers made a damn good character]
Major Thyris th'Shar: Following Sholi's adept handling of first contact with the Andorians a few years earlier, great strides has been made in forging new working relationships with them, as such they were given the chance to have a representative on the NX-01 to help solidify their good public relations. Th'Shar was appointed as the Chief Science Officer. Though far from a great supporter of the Andorian-Earth relationship, as well as having great misgivings about the Vulcans, he is one of the Imperial Guard's best scientists (his superiors also see it as a test, if someone like him can get along with the primitive humans and condescending Vulcans then anyone can).
Lieutenant (jg) Travis Mayweather: The ship's Helmsman, he often tells about how he learned how to fly before he could walk. The twenty-something Boomer who has been to more worlds and travelled more light-years than any of the other humans onboard, he is a font on knowledge and tall tales. Though this is his first posting his vast experience and exceptionally piloting skills saw him jump the rank of ensign entirely. Despite his vast wealth of experience he is still a young man and often lets his enthusiasm and exuberance get the better of him.
Lieutenant (jg) Hoshi Sato: Her uncanny ability to pick up new languages and perform translations faster than the universal translator made her Sholi's only choice for Chief Communications Officer. Despite her rank, she hasn't spent any time on starships, having been assigned as an instructor or translator on Earth, as such the dangers and realities of life in space prove to be a little much for her at times, but she is determined to tough it out and prove she has what it takes and doesn't want to let Sholi down--especially after all the faith she has placed in her. [Again not really all that different from what was on the show, Hoshi was a character I also liked, though with some more consistency here]
Doctor Phlox: Again a character who is pretty much how he is in the show, though I would say make him weirder, how he approaches situations or looks at things from a very different perspective, to give the humans on the ship a unique POV that they would never have considered. [See Trip and Hoshi]