[Lots of Pictures] Idle to Run Animation Delay? When Pressing Forward Slides forward without Animation

Hi I'm very new to 3D animation/game programming! My questions is for transitioning from my idle animation to my run animation. If I press the "UP" key or "W" key the character slides forward without the animation playing. I believe it takes about a half second - one second for the animation to kick in.

How can I remove the or reduce the delay between switching these animations?

I hope this question makes sense I will attach some images and a GIF. Please let me know if I need to provide anymore information or if there is something I should have read before bringing up this question!

GIF: http://gph.is/1PzY4Zu

Animation Controller: Script:

using UnityEngine; using System.Collections;

 public class newScript : MonoBehaviour {
     private Animator anim;
     private CharacterController controller;
 
     public float speed = 6.0f;
     public float turnSpeed = 60.0f;
     private Vector3 moveDirection = Vector3.zero;
     public float gravity = 20.0f;
 
     // Use this for initialization
     void Start () {
         anim = gameObject.GetComponentInChildren<Animator>();
         controller = GetComponent<CharacterController>();
     }
     
     // Update is called once per frame
     void Update () {
         if (Input.GetAxis("Vertical") == 1)
         {
             anim.SetInteger("animParm", 1);
         }
         else
         {
             anim.SetInteger("animParm", 0); 
         }
 
         if (controller.isGrounded)
         {
             moveDirection = transform.forward * Input.GetAxis("Vertical") * speed;
             if(Input.GetKey("space"))
             {
                 moveDirection.y += gravity*25;
             }
         }
 
         float turn = Input.GetAxis("Horizontal");
         transform.Rotate(0, turn * turnSpeed, 0);
         controller.Move(moveDirection);
         moveDirection.y -= gravity;
     }
 }