Moving 2D sprite along a path

I have 10 x 10 grid with some items (Gems). Player drags cell Item from one place to another. I have already found Vector3 positions where I should move my game object. As I understand I should do this in Update method by calling Vector3.MoveTowards or Vector3.Lerp or changing position directly, but I have started using Unity not so long ago and I didn't quite get how should I do this. So I have List with positions where I should move my object (Debug.DrawLine)

How can I successively move Item from one point to another and what method I should use to do this?

UPD. Seems this is working for me. Maybe someone have more correct way to do this

 void Update () {
         if (currentItem != null) {
             currentItem.transform.position = Vector3.MoveTowards(currentItem.transform.position, nextCellPosition, Time.deltaTime * 4.0f);
 
             if (currentItem.transform.position == nextCellPosition) {
                 activePath.Points.RemoveAt(0);
 
                 if (activePath.Length > 1) {
                     nextCellPosition = cells[activePath.Points[1].y, activePath.Points[1].x].transform.position;
                 } else {
                     cells[activePath.Points.First().y, activePath.Points.First().x].Item = currentItem;
                     currentItem = null;
                 }
             }
         }
     }