Well, over a decade ago I gave a lot of thought. This was before Enterprise was announced. I even designed ( well "kitbashed" ) the uniforms and the ship. ( modified after ENT)
It was set during the NCC-1701 Enterprise's first mission commanded by Captain Robert April.
The crew:
Captain Robert April: A tough maverick commander who started his career as an enlisted man. Born on the New Tasman Colony April joined Starfleet to escape the boredom and drugery of colonial life. Rising to the rank of Chief Petty Officer, he was given a battlefield promotion to assume command after his ships commader was killed and later attended Starfleet's OCS program, receiving an officer's commision.
Dr. Sarah Goldman: A former child progidy of Israeli-Ethiopean decent, Goldman holds advanced degrees in Medicine, Psychology and Physics. Feeling unchallenged in academia Goldman joined Starfleet in the hope of fully utilizing her gifts, skills and knowlege and to be on the cutting edge of new discoveries. She serves as the Enterprise's Chief Medical Officer and Science Officer.
Commander Nogura: The ships XO and a by-the-book officer who's uncomfortable with Aprils maverick tendancies. Its an open secret that he was assigned to the Enterprise to curb those tendancies. Norgura comes from a powerful political family who hold various positions in the governments of Earth and the Federation. They see Starfleet as a stepping stone to politics and have begun to pressure Nogura to leave the service. I figure there would be some conflict between April and Nogura, with Nogura being right on occasion and winning some begrudging respect from April. The "political family" angle would also figure in storylines where UFP politics come into play
Nogura is also a key member of the ships first contact team because he does have a flair for diplomacy.
Lt. Commander Slev: An Andorian, who was Aprils choice to be XO, Slev servs as the ships Security Cheif. Slender and soft spoken, Slev is often underestimated by opponates unfamiler with Andorian warrior culture. Slev is also a poet, coming from the Andorian Warrior-Poet tradition.
My Andorians are a caste based Matriarchy. Each family/social unit is comprised of a female and groups of three males from different castes called a triad. The bond between the males is very deep and can only be broken by death. The number of triads bonded to each female varies. All males become part of their father's caste. (Somehow they know which member of the triad is the father) All females are raised seperate from the males to become matriarchs. The Matriarchal Council that rules Andor is comprised of the most powerful females.
Slev's triad was killed and he is "bond-broken". His membership in the Warrior caste led him to Starfleet, which is one of the few places that will accept a bond broken Andorian. He thinks of April and the Chief as his triad bond brothers, even though he is no longer bonded to a matriarch. Sorry, no ice powers.
The Chief Moq: A Tellerite he's the top non-commisioned officer on the ship and runs engineering. A former drill instructor at Starfleet's boot camp he terrifies most of the junior crewman who live in fear of a temporay assignment to Engineering. He's also April's oldest friend.
Lt. Chris Pike: The ships helmsman. Devoted, loyal and a bit too serious he would literally lay down his life for the Captain, the ship and the crew. April thinks he need to loosen up and trust his instincts more.
Lt(jg). Maggie Garcia: Quiet and shy, she is ironically the ship Communications Officer. Unknown to most of the crew, Garcia is a decendent of the Eugenic supermen who plunged Earth into war centuries ago. Smarter and stronger than most humans, but raised in isolation by scientists, Garcia is socially awkward and at times uncomfortable with "normals" and fears their reaction to her background. April, whose ancestors fought and died in the Eugenics Wars, isn't pleased to have her aboard. Goldman is her "sponser" and one of the chief designer of the program to "mainstream" Eugenic Humans. Garcia was the number one candidate for this program.
Anyone known to have an augment background is pretty much kept under lock and key by the Government of Earth. (The UFP turns a blind eye to this "internal matter") Part of the reason for this is the augment process causes various mental problems ( paranoia, megalomania, sociopathic tendancies). Garcia is on an experimental drug regimen to keep this under control. Which probably contributes to her shyness and quite demeanor. All the above would be plot points for various episodes and arcs.
Ensign Guinevere "Lou" Llewellyn: Garcia's roommate and polar opposite. Llewellyn serves as ship's Navigator. Loud, loquacious and uninhibited Lou is an interstellar incident waiting to happen. A Starfleet brat, who mother is an Admiral, Lou has probably logged more space hours and been on more planets than all but the most experienced crewmen. Any hope by her parents that Starfleet would temper her attitudes have thus far been proven false.
The main antoganists would have been the Orions.