Mouse controlled controller

Unity Engine
1

I’m currently trying to make a game where the character follows the mouse pointer. but I want the character to lag behind the mouse a little bit (a set speed). I also don’t want this character to travel in the X Direction. that way it doesn’t travel forward. here’s my code so far :

using UnityEngine;
using System.Collections;

public class ShipControl : MonoBehaviour
{
    public float distance = 1.0f;
    public bool useInitalCameraDistance;

    private float actualDistance;
    // Use this for initialization

void Start () {
        if (useInitalCameraDistance) {
            Vector3 toObjectVector = transform.position - Camera.main.transform.position;
            Vector3 linearDistanceVector = Vector3.Project(toObjectVector,Camera.main.transform.up);
            actualDistance = linearDistanceVector.magnitude;
        }
        else
        {
            actualDistance = distance;
  
        }
    }
    void Update ()
    {
        Vector3 mousePosition = Input.mousePosition;
        mousePosition.z = actualDistance;
        transform.position = Camera.main.ScreenToWorldPoint(mousePosition);
    }
}

It works except the stuff I mentioned above. Any tips? (this is a flying object, so Up, Down, Left, Right are need. but not Forward or backwards)

2

These could be used for adding delay: