Rotate Character towards Movement Direction

Might seem like a relatively simple thing but it's just not working for me, all the answers I've found online do not work.

I want my character to face the direction he moves when strafing, moving forwards, or backwards. Quaternion.LookRotation causes him to spin rapidly and I can't feed a transform.Rotate(moveDirection) into Y only when he needs to move for both X and Z

 using UnityEngine;
 using System.Collections;

 [RequireComponent(typeof(CharacterController))]
 [RequireComponent(typeof(Rigidbody))]
 public class PlayerMovement : MonoBehaviour
 {
     public CharacterController characterController;
     public Animator anim;
     public Camera cam;

     public float moveSpeed = 5f;
     public float turnSpeed = 15f;
     public float gravity = 21f;
     
     private float h;
     private float v;
     private float s;
     private float mh;
     private float mv;
     private float deadZone = 0.1f;
     private Vector3 moveDirection = Vector3.zero;
     private Vector3 turnDirection = Vector3.zero;

     void Awake()
     {
         //need access to the character controller and animator
         anim = GetComponentInChildren<Animator> ();
         characterController = GetComponent<CharacterController> ();
         cam = Camera.main;
     }

     void Update()
     {
         //cache the inputs
         h = Input.GetAxis ("Horizontal");
         v = Input.GetAxis ("Vertical");
         s = Input.GetAxis ("Strafe");
         mh = Input.GetAxis ("Mouse X");
         mv = Input.GetAxis ("Mouse Y");

         moveDirection = Vector3.zero;

         //check if it's grounded, otherwise player cannot move, also check for the deadzone
         if(characterController.isGrounded)
         {
             ProcessVerticalMovement(v);
             ProcessHorizontalMovement(h, mh, s);

             //normalize the diagonal inputs to prevent values above 1
             if (moveDirection.magnitude > 1)
             {
                 moveDirection.Normalize ();
             }

             moveDirection = transform.TransformDirection(moveDirection);
         }



         //set the animator's Speed float to the magnitude of the moveDirection to allow for the run animation to play
         anim.SetFloat ("Speed", moveDirection.magnitude);

         //calculate gravity
         moveDirection.y -= gravity * Time.deltaTime;

         //move the character

         characterController.Move (moveDirection * moveSpeed * Time.deltaTime);
         transform.Rotate(turnDirection * Time.deltaTime);
         transform.Rotate (0f, moveDirection.x, 0f);
         //transform.rotation = Quaternion.LookRotation(moveDirection);
     }

     void ProcessVerticalMovement(float v)
     {
         if (v > deadZone || v < -deadZone)
         {
             moveDirection = new Vector3 (0f, 0f, v);

         }
     }
     
     void ProcessHorizontalMovement(float h, float mh, float s)
     {
         
         //if player is holding RMB while horizontal input then strafe
         if((s > deadZone || s < -deadZone) || (Input.GetButton("CameraTurn") && (h > deadZone || h < -deadZone)))
         {
             Debug.Log ("strafing");
             if(s > deadZone || s < -deadZone)
             {
                 moveDirection.x = s;
             }else
                 moveDirection.x = h;

         }
         //if player is pressing horizontal input then turn, or if player has RMB down (but not horizontal input) then turn
         if(Input.GetButton("CameraTurn") && (mh > deadZone || mh < -deadZone))
         {
             turnDirection = new Vector3(0f, mh * 200f, 0f);

         }else if(!Input.GetButtonDown("CameraTurn") && (h > deadZone || h < -deadZone))
         {
             turnDirection = new Vector3(0f, h * turnSpeed, 0f);

         }else
             turnDirection = Vector3.zero;

     }
 }