For a small ship of around the era you're looking for, I'd suggest the Archer or Curran classes from the amazing Starfleet Museum. You may have to fudge the dates a bit but it looks VERY good and is about the right size at twenty-something crewmembers. Personally, I just love the design of the Wasp class, but it might be a bit too big for what you have in mind, with 100+ crew.
For your players, I would of course get them to play whatever they enjoy, including maybe for your first player a Starfleet officer of Commander rank for CO, since the ship is too small to warrant a full Captain. For your second player, I'd ask if she/he'd be interested in a Vucan Engineer, either over-protective of his precious Vulcan engines, or else forced to work with inferior Human technology.
For your third player, I'd consider letting him/her design an observer from a completely new race, sidestepping potential continuity problems with the Andorians. Maybe something along the lines of Phlox, maybe something as alien as you both can make it, maybe something to balance out your other two characters.
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