The Ship.
Developed by the United Earth Military Authority (UEMA) as a pure combat vessel, the Declaration class is designed to protect Earth and it's colonies from alien aggression. With the project running over budget and behind schedule, UEMA turns to the United Earth Space Probe Agency for funding and resources. As a result of this uneasy alliance, the last ship of the initial production run, Enterprise, is adapted to serve as a deep space research and exploration vessel. Nominally under UESPA control, it must still perform military tasks when required.
Characters.
CO: Captain Jackson 'Jacko' Archer. American. UESPA.
Having participated in numerous exploration missions, including first contact with the Denobulans, Archer is an ideal choice for command. He is less comfortable with the ship's military role, and relies heavily on his first officer.
XO: Commander Maria Hernandez. Mexican. UEMA.
Career military. In addition to her job as XO she acts as the ships chief tactical officer. Occasionally her focus on military solutions will bring her into conflict with the captain's more peaceful approach. Is a practising (not lapsed!) Catholic.
Chief Engineer: Commander Charles 'Trip' Tucker III. American. UESPA.
Don't let his Southern accent and good old boy ways fool you. Trip has a brilliant mind, and studied high energy physics at Cambridge. An old friend of the captain, Trip can be relied upon to back up Archer's decisions. Also acts as second officer.
Helm Officer: Lt. Commander Travis Mayweather. Canadian. UEMA
Cocky to the point of arrogance, Travis
knows he's the best helmsman in space. Unhappy to be assigned to what he sees as a 'babysitting job', he'd much rather be on a combat posting, and let's everyone know it. Only came along because he was promised his choice of post after his first tour was up. Of course, when he sees what the Enterprise gets into, he may just decide to stick around...
Communications Officer. Lt. Hoshi Sato. Japanese. UESPA.
In addition to her skills as a linguist, Sato is a trained diplomat. As such, she's the captain's right hand woman during first contact missions, trade negotiations and the like.
Marine Commander. Lt. Malcolm Reed. New Zealand. UEMA Marine Division.
A tough Kiwi, Reed is in charge of the detachment of marines assigned for security on the ship. Like Travis he is initially unhappy about the posting, and suspects that it is essentially punishment after he and his men completely trounced a much larger, supposedly superior force during a training exercise. The opposing force's commander was on his fast track to promotion until the defeat, and pulled a few strings to get Reed's unit assigned to a supposed dead end assignment.
As an aside, whilst the unit is referred to as 'Mako's', that's just a nickname, a reference to the shark. It does not stand for anything.
Surgeon. Doctor Philip Locke. American. Civilian.
Whilst the ship has a couple of Corpsman on board, and the Mako's have their own medics, Archer was unwilling to start his mission without a fully trained doctor on board. Despite his gruff, no nonsense manner, Dr. Locke is an ideal choice. In addition to twenty years experience, he has recently participated in the cross species medical program, giving him a familiarity with alien species unmatched by any other Earth physician.
Scientific Advisor. Professor Polly 'Mycroft' Partridge. British. Civilian.
An old friend of Trip's from his Cambridge years, getting Polly on board was a real coup. Although best known as an astrophysicist, she posses an astonishingly high IQ, and has degrees in numerous scientific disciplines. Her nickname was bestowed upon her at university by a fellow student who was fond of the Sherlock Holmes stories, and refers to a description of Holmes' elder brother "Other men are specialists, but (Mycroft's) specialism is omniscience".
Unlike the cool, calculating 'ice maiden' type seen with 7of9 and T'pol, Polly is wildly enthusiastic about the universe, and loves science because it helps us understand the cosmos more completely. Despite their differing philosophies (Polly is a pacifist and entirely Atheist), she get's on well with Hernandez, eventually forming a deep friendship.
To avoid her becoming too much of a Mary Sue, she can't sing or play a musical instrument, isn't good with animals and is absolutely useless in a fight, though she may learn some martial arts moves from Maria, as the series progresses.
Oh, and she fulfils the HOT LOOKING CHICK to get the 14 year olds watching criteria. In fact, given her quirky sense of humour, plus her love of 20th century TV and movies, she may even wear a catsuit (think Emma Peel, Trinity or Selene. Or possibly even Wilma Deering!)

.
In addition there should be several other recurring characters. A couple more civilian scientists, a civilian chef who acts as unofficial moral officer, plus a few crew both UEMA and UESPA who crop up regularly.
There should also be at least two gay characters amongst them, though this shouldn't be used a plot point. About half way through the first season, it becomes obvious that, for example, one of the Mako's is seeing the assistant chief engineer.