Captain: Malcom Reynolds. I was tempted to chose Sisko for his talents as a tactician, but since we’re working with a largely civilian crew I suspect that Reynolds would be laid back enough to run a tight, responsible ship without pissing anyone off more than the job requires.
First Officer: This was the hardest to decide, but I think I’ll go with Susan Ivanova: she’s thick-skinned, which will let her put up with Reynolds, and she’s incredibly anal, which will let her pick up any slack that Malcom’s looser command style leaves.
Helmsman: Seven of Nine. Defiant-style navigation systems will probably rely on proficiency more than split-second reflexes, and Seven has the calm, analytical mind needed to excel at the task, a dedication to duty that’ll keep her from getting bored, and via her borg implants an insane corpus of scientific knowledge she can pull out whenever they run into an anomaly.
Chief Enlisted Officer: Miles O’Brien all the way. He’s smart, savvy, responsible, and a drunk scotsman. What more could you ask for?
Head of Security: Michael Garibaldi, because you can’t go wrong with a lawful good security chief who mentally translates “black ops” as “white ops, only more efficient”. I’ll stock my pantry with synthale so he can indulge his raging alcoholism without getting any of his screwup on my starship. 
Chief Engineer: The Traveler. If this is my starship I’d like to emphasize innovation over reliability, and you just can’t beat having your engine run by a guy who can alter warp fields with his mind.
Assistants to the chief engineer: B’Elanna Torres and Kaylee Frye. Torres has that perfectionist streak to keep the engine room working smoothly and the freakish strength to keep the crew in line, and Kaylee’s eccentric genius will probably catch any mistakes that the Traveler or B’Elanna make.
Chief Medical Officer: Simon Tam. He’s a brilliant surgeon, flexible enough to do what needs to be done to help people, and anal retentive enough to be an effective administrator and manager. Plus, he comes with a sister-shaped accessory that is essential to ship’s operations.
Ship’s Mascot: River Tam. Cute and personable enough to keep morale up, crazy and scary enough to keep the roughs in line, and always ready to be foolishly ignored by the bad guys until it’s too late.
Science team: Rather than a single science officer, I would use a think tank staffed by Dr. Who, Lieutenant Barkley, Q, Scotty, River, and Seven (when she’s not at the helm). Scotty is very diplomatic, so he can also serve as the go-between and brief the senior staff on what the hell his people are up to.
Talia Winters: I don’t know what she’ll do, but I want her on my ship.