As far as I know, you don't have a default gun mechanics in Unity. That's your job here
I've made some shooters, not FPS's though, but the mechanics should be the same: You have your character (with a CharacterController component attached, perhaps) moving and such stuff, and, when you get input from your "Fire" button, you instantiate your projectile and add a force and... You know the rest, BANG!
As for the projectile, be aware that Raycast won't be visible, unless you cast a LineRenderer (or so I'd do), and it's function is to detect whether an object could collide with another. You would probably want to create a prefab with a non-kinematic Rigidbody. Remember to add a collider.
Hope this helps.