The title is self-explanatory. My choices:
Owner: Tony Stark (Iron Man series)
Other possibilities: Adrian Veidt (Watchmen), Jay Gatsby (The Great Gatsby), Willy Wonka (Charlie and the Chocolate Factory), Scrooge McDuck (Disney character)
Stark is wealthy -- his net worth is estimated at $8.8 billion. More importantly, he invests that wealth in high-level research and development, constantly searching for the next breakthrough. Maybe Stark Industries develops a new set of spikes to enhance speed and mobility. Or an undetectable PED to help our heroes slug the ball even farther. He would be a Mark Cuban type owner, involved but not meddlesome. Stark Expo 2010 was held in Flushing Meadows Park, and was a rousing success. A Mets World Series Championship just a few minutes walk away from the park would be a fitting end to the annual Expo.
General Manager: Obi-Wan Kenobi (Star Wars series)
Other possibilities: Hermione Granger (Harry Potter series), Stringer Bell (The Wire), Miranda Priestly (The Devil Wears Prada), Spock (Star Trek series), Ender Wiggin (Ender's Game)
General Kenobi is charismatic and judicious, a true leader of men. His Jedi powers of persuasion would be helpful at the trade deadline and during negotiations with Scott Boras. Old baseball man Yoda would also have his ear. [Insert joke about lightsabers/sabermetrics]. And he's a great quote, so he won't have to jump in an airplane with no access to a cell phone anytime something major happens (like our current GM).
Manager: Lou Brown (Major League series)
Other possibilities: George Knox (Angels In The Outfield), Pop Fisher (The Natural), Sal Martinella (Rookie Of The Year), Uchiyama (Mr. Baseball)
The above picture displays Brown's unique but effective motivational tactics. He has the respect of the clubhouse and isn't afraid to give young players a shot over proven veterans. Plus he would never tolerate that olé bullsh** from David Wright.
Team Doctor: E.T. (E.T. the Extra-Terrestrial)
Other possibilities: John Coffey (The Green Mile), Doogie Howser (Doogie Howser, M.D.), Mark Greene (ER)
Let's not mess around here. Let's go straight to the god-like character who can heal anything with the touch of a finger. Sure, he's sort of creepy looking and doesn't speak earth languages very well, but that will be forgotten the first time a concussed player can take the field just minutes after getting a facial from the outfield wall. E.T. can travel to and from his home planet as he pleases.
Team Spokesman/Public Relations Director: Atticus Finch (To Kill A Mockingbird)
Other possibilities: Nick Naylor (Thank You For Smoking), Jake Brigance (A Time To Kill), Hawkeye Pierce (M*A*S*H)
Atticus is near the top of the list of fictional heroes. When he speaks, there is no circumlocution, no "Citi Field has no obstructed views" type baloney. This is a man who can be trusted. He would function almost as the ombudsman of the Mets, stressing honesty with the fans/customers over toeing the company line.