Player Rotation and movement

I'v been trying to add rotation and movement towards the way the character is facing, without breaking the physics or locking the character. After hours of googling/youtube and experimentation on how to implement this im back for help again >_<. This is the closest the closest i got to it actually working.The character is rotating but its drifting and moving to the way he's facing but the rotation is awful.. Can someone expainto me what im doing wrong and what the best solution is. This is my first script and im trying to understand and figure things out.

using System.Collections; using System.Collections.Generic; using UnityEngine;

public class PlayerMovement : MonoBehaviour {

 //VARIABLES
 
   //MOVEMENT//SPEED
 [SerializeField]  private float moveSpeed;
 [SerializeField]  private float walkSpeed;
 [SerializeField]  public float runSpeed;
 [SerializeField]  public float rot;
 [SerializeField]  public float rotSpeed;
 [SerializeField]  public float smooth;
 public float turnSmoothTime = 0.1f;
 
 
   //GRAVITY
 [SerializeField] private float jumpHeight;
 [SerializeField] private float gravity;
 public bool isGrounded = true;
 //    [SerializeField] private float groundCheckDistance; 
  //[SerializeField] private LayerMask groundMask; 
   // Variable for Layer for groundcheck
 
 private Vector3 moveDirection;
 private Vector3 velocity;
 private Animator anim;
 Rigidbody rb;
 
 
 //REFERENCES
 private CharacterController controller; 
 
 private void Start()
 {
     //Debug.Log("Start");
     controller = GetComponent<CharacterController>();
     anim = GetComponent<Animator>();
     rb = GetComponent<Rigidbody>();
         }
 
 

   void OnCollisionEnter(Collision theCollision)
  {
      if (theCollision.gameObject.tag == "Plane")
      {
          isGrounded = true;
          print("grounded");
                  }
  }
 
 
  void OnCollisionExit(Collision theCollision)
  {
      if (theCollision.gameObject.tag == "Plane");
      {
          isGrounded = false;
           print("not grounded");
      }
  }
 private void Update()
 {
     //rot += Input.GetAxisRaw("Mouse X") * rotSpeed * Time.deltaTime;
         //transform.eulerAngles = new Vector3(0, rot, 0);
      //rotation
     

     
                         
     //Debug.Log("test");
     Move();
     
 }

 private void fixedUpdate()

 {

 }

 
     
 //MOVEMENT
 private    void Move()
 {       
     
         
                     
         float moveZ = Input.GetAxisRaw("Vertical");
         float ad = Input.GetAxis("Horizontal");
         //float rot = Input.GetAxis("Mouse X");
            
         
                
             moveDirection = new Vector3(ad, rb.velocity.y, moveZ);
             
         
         if(isGrounded == true)  
         {
             
                                                  
              
             if(moveDirection != Vector3.zero && !Input.GetKey(KeyCode.LeftShift)) 
             
             {
                 
                 //Walk
                 Debug.Log("Walk");
                 walk();
             }    
             else if(moveDirection != Vector3.zero && Input.GetKey(KeyCode.LeftShift))
             {
                 
                 anim.SetFloat("JumpAnim", 0); //Animation stop
                 //Run
                 run();
                 Debug.Log("run");
             }
             else if(moveDirection == Vector3.zero)
             {
                 //Ìdle
                 anim.SetFloat("JumpAnim", 0);
                 idle();
                 
             }    

             if (Input.GetButtonDown("Jump") && isGrounded)
              {
                  //Animation stop
                  //Jump
                  jump();
                  
              }

     
          
         }
         
         //transform.rotation =Quaternion.LookRotation(transform.up * rotSpeed * rot);
         //rb.AddTorque(transform.up * rotSpeed * rot);
         //float targetAngle = Mathf.Atan2(moveDirection.x, moveDirection.z) * Mathf.Rad2Deg;
         //float angle = Mathf.SmoothDampAngle(transform.eulerAngles.y, targetAngle,ref smooth,turnSmoothTime);
         //transform.rotation = Quaternion.Euler(0f,angle,0f);
         float rot = Input.GetAxis("Mouse X");
         moveDirection = transform.TransformDirection(moveDirection);
         rb.AddTorque(transform.up * rotSpeed * rot);
         
            
         
         rb.velocity = new Vector3(moveDirection.x * moveSpeed, rb.velocity.y, moveDirection.z * moveSpeed);
         
         
         
     //transform.rotation = Quaternion.Euler(0f,0,0f);
 }
 
 private    void idle()
 {
     Debug.Log("Idle");
     float MMY = Input.GetAxis("Vertical");
     anim.SetFloat("InputY",MMY );  //
 }    
 private    void walk() /////WALK 
     {
         moveSpeed = walkSpeed;
         anim.SetFloat("run", 0);
         Debug.Log("walk");
     float MMX = Input.GetAxis("Horizontal");
     float MMY = Input.GetAxis("Vertical");
     
     
     anim.SetFloat("InputY",MMY);
     anim.SetFloat("InputX",MMX);
 }

 private    void run() ///// RUN
 {
     
         moveSpeed = runSpeed;
         anim.SetFloat("run", 1);
         float MMX = Input.GetAxis("Horizontal");
         float MMY = Input.GetAxis("Vertical");
         anim.SetFloat("InputY",MMY);
         anim.SetFloat("InputX",MMX);

 }
 private void jump()
 {
     anim.SetFloat("JumpAnim", 1);
     Debug.Log("jump");
      //rb.AddForce(0, 0, jumpHeight, ForceMode.Impulse);

      rb.AddForce((Vector3.up) * jumpHeight, ForceMode.Impulse);
     // rb.AddForce(0, 0, jumpHeight, ForceMode.Impulse);
     //velocity.y = Mathf.Sqrt(jumpHeight * -2f * gravity); //
     

 }
  
   

 

 
 

}