How to make a half 2d- half 3d main menu??

The resolution can be as $$anonymous$$gh as the resolution of the screen being used..

The easiest way to create your background texture is probably with a plane, just create a plane and add the texture, and line it up with the camera.

Now as for the 3D object, just drop it in place in front of the plane, then add a simple script such as:

 function Update(){
 var $$anonymous$$t : RaycastHit;

     if(Physics.Raycast(Camera.main.ScreenPointToRay(Input.mousePosition),$$anonymous$$t)){
          if($$anonymous$$t.name == "Name of the object")
          $$anonymous$$t.transform.Rotate(Vector3.up * Time.deltaTime);
     }
 }

(for t$$anonymous$$s example, the object needs a collider to work)