Need Help: Walking toward rotation of mouse x

Unity Engine
1

I have a script where I can strafe left and right with arrow keys, and move forward and back as well.

I’m trying to get the forward to be relative to rotation set to mouse position x.

I have this: below;

but am looking for a more simple way as the turn doesn’t react as quickly as I need an on release of button it snaps back.

using UnityEngine;
using UnityEngine.UI;
using System.Collections;

public class PlayerMovement : MonoBehaviour {

    Animator anim;
    Rigidbody rb;
    Vector3 hitr;
    Vector3 hitrn;
    Vector3 player;
    Quaternion TargetRotation;

    float speed = 150f;

    public float turnInput = 50f;
    public float rotateVel = 50f;

    public Quaternion targetRotation
    {
        get { return TargetRotation; }
    }

    void Start()
    {
        TargetRotation = transform.rotation;
        rb = GetComponent<Rigidbody> ();
        anim = GetComponent<Animator> ();
    }

    void Update ()
    {
        Move ();
        Turning ();

    }

    void FixedUpdate()
    {
        //inclines
        RaycastHit hit;
        Physics.Raycast (transform.position, Vector3.down, out hit);
        if(Physics.Raycast(transform.position, Vector3.down, .5f))
        {
            transform.up = hit.normal;
            hitrn = hitr - transform.eulerAngles;
            transform.Rotate(hitrn.x, 0, hitrn.z);
        }
    }


    void Move()
    {
        float forward = Input.GetAxis ("Vertical"); 
        anim.SetFloat ("Speed", forward);
        float sideways = Input.GetAxis ("Horizontal");
        anim.SetFloat ("Direction", sideways);

        Vector3 movement = new Vector3 (sideways, 0f, forward);
        rb.AddForce (movement * speed);

    }

    void Turning()
    {
        float turn = Input.GetAxis ("Mouse X");

        if (Input.GetKey(KeyCode.Mouse0))
        {
            TargetRotation *= Quaternion.AngleAxis (rotateVel * turn * Time.deltaTime, Vector3.up);
            transform.rotation = TargetRotation;
        }       
    }
}
2

This should work:

Vector3 movement = (transform.forward * forward) + (transform.right * sideways);
3

@GroZZleR
This does work to an extent. If I switch animation from no weapon to weapon/weapon aim it doesn’t save the rotation of the character. I cannot get camera to rotate with it either. If I child the camera the camera itself rotates way to much. Other wise it does function with default animation state.