My current setup is based on the 3DBuzz 2D shooter tutorials, so it doesn’t quite work in my 3rd person shooter: I want the projectile to move in the direction the ship was facing when the projectile was spawned, but at the moment I’m stuck with Vector3.Up which is sort of useless. 
How can I tell the projectile inside the projectile script that is attached to it that I want it to move in the direction the player is facing (down its Z Axis)?
Are you looking for transform.forward?