unity - Move rigidbody using WASD keys but rotate it based on camera/mouse movement

I am very new to unity and my scripts are based on some scripts found on the web.

I want to make a first person view so the camera is attached to my rigidbodys head. Then i want to move my rigidbody based on keyboard input (wasd) and rotate it using the mouse movement.

Until now, i used the following code for moving my rigidbody:

void Update() {

    /* calculate rigidbody movement */

    movement = new Vector3( Input.GetAxisRaw("Horizontal"), 0, Input.GetAxisRaw("Vertical")).normalized;

    /* calculate mouse look to rotate the rigidbody*/
    mouseDelta = new Vector2(Input.GetAxisRaw("Mouse X"), Input.GetAxisRaw("Mouse Y"));
    mouseDelta = Vector2.Scale(mouseDelta, new Vector2(sensitivity * smoothing, sensitivity * smoothing));
    smoothV.x = Mathf.Lerp(smoothV.x, mouseDelta.x, 1f / smoothing);
    smoothV.y = Mathf.Lerp(smoothV.y, mouseDelta.y, 1f / smoothing);
    mouseLook += smoothV;

}


void FixedUpdate() {   

    /* apply rigidbody movement from Update() */
    transform.Translate( movement * moveSpeed * Time.deltaTime );        
    /* apply rigidbody rotation from Update() */
    transform.localRotation = Quaternion.AngleAxis(mouseLook.x, transform.up);        
    /* apply camera rotation from Update() */
    Camera.main.transform.localRotation = Quaternion.AngleAxis(-mouseLook.y, Vector3.right);  


}

I learned today that i dont have to move a rigidbody's transform but now i am totally confused and it seems i have to restart my whole (first!) project.

So when i use MovePosition and MoveRotation, how do i rotate it based on the camera perspective/mouse movement?

I think the movement Vector is ok so i can simply rewrite the FixedUpdate to something like

rigidbody.MovePosition(movement * speed * Time.deltaTime)

but i am totally stuck on how to apply the camera rotation to my rigidbody to use it like

void FixedUpdate() { 
    /* move the rigidbody */           

    rigidbody.MovePosition(movement * moveSpeed * Time.deltaTime);
    /* rotate the camera */
    camera.transform.localRotation = Quaternion.AngleAxis(-mouseLook.y, Vector3.right);

    /* but how can i rotate the rigidbody based on the cameras rotation??? */
    rigidbody.MoveRotation(?????);

}

I hope its clear what i want, thank you!