Unity Simple First Person Controller

FirstPersonController.cs

using UnityEngine;

public class FirstPersonController : MonoBehaviour
{
    [SerializeField] private float _speed = 5;
    [SerializeField] private float _sensitivity = 1;
    [SerializeField] private float _clampRot = 85;
    [SerializeField] private bool _lockCursor = true;

    [SerializeField] private float _cameraSmoothing = 0.25f;
    [SerializeField] private float _directionSmoothing = 0.25f;

    private Transform _camTransform;
    private Vector2 _mouseInput;
    private Vector2 _currentMouse;
    private Vector2 _mouseVel;

    private Vector3 _currentDir;
    private Vector3 _dirVel;

    private void OnValidate()
    {
        _camTransform = Camera.main.transform;
    }

    private void Start()
    {
        if (_lockCursor)
        {
            Cursor.lockState = CursorLockMode.Locked;
            Cursor.visible = false;
        }
    }

    private void Update()
    {
        Move();
        Rotate();
    }

    private void Move()
    {
        Vector3 dir = new Vector3(Input.GetAxisRaw("Horizontal"), 0, Input.GetAxisRaw("Vertical"));
        _currentDir = Vector3.SmoothDamp(_currentDir, dir, ref _dirVel, _directionSmoothing);
        transform.position += _camTransform.TransformDirection(_currentDir) * _speed * Time.deltaTime;
    }

    private void Rotate()
    {
        _mouseInput += new Vector2(Input.GetAxis("Mouse X"), -Input.GetAxis("Mouse Y")) * _sensitivity;
        _mouseInput.y = Mathf.Clamp(_mouseInput.y, -_clampRot, _clampRot);
        _currentMouse = Vector2.SmoothDamp(_currentMouse, _mouseInput, ref _mouseVel, _cameraSmoothing);

        transform.rotation = Quaternion.Euler(0, _currentMouse.x, 0);
        _camTransform.localRotation = Quaternion.Euler(_currentMouse.y, 0, 0);
    }
}

How to use

Create a Player GameObject and make the Camera the child of the Player.
Add this script to the Player GameObject.