Something to call their own
I would also put forward the idea that player's love to have something to call their very own. Every time the Defiant is mentioned , everyone will think "Sisko's Ship" or "The ship from DS9". Give the players something to call their own.
I always try to begin with either a rarely seen canon ship class (New Orleans, Daedalus, etc.) or an entirely new vessel designed by my players and/or myself. This way the group cares for the ship like it's their baby and really feels it when the ship is damaged or in danger.
AndorMan
Truth, Justice and the Andorian Way