Third person climbing?

None of the answers that I found on internet helped me. Please I hope that you can help. So basically I want to implement climbing on the object just like in GTA SA(for example I want to climb on custom box which is more or less my height or a bit less/or a table for instance). How do I make animation look natural? How do I naturally place the body,hands and feet depending on the height?

So I begun writing a function, but I realized that I can't answer those questions above.

  ray = new Ray(transform.position,transform.forward);
             if (Physics.Raycast(ray,out hit,rayCastDist,grabbableLayer))
             {
                 CalculateTangent();
                 Debug.DrawRay(transform.position,ray.direction);
                 //get height and width
                 GameObject hitObject = hit.collider.gameObject;
                 if (hitObject.GetComponent<BoxCollider>())
                 {
                     BoxCollider box = hitObject.GetComponent<BoxCollider>();
                     //transform.eulerAngles = tangent;
                     float height = hit.transform.localScale.y * ((BoxCollider)hit.collider).size.y;
                     float width = hit.transform.localScale.z * ((BoxCollider)hit.collider).size.z;
                     if (heightOfJump > height && width>minWidth&&!isInGrabbingStage)
                     {
                         Debug.Log("Grab");
                         //ClimbOverFence();
                     }
                 }