Top-Down Movement in Unity

I am attempting to make a top-down 2D character with a circle collider on the XZ plane.

The problems/features I need to deal with are:

1. I want the character to always face the mouse, to rotate to look at the mouse.

2. I want the character to move dependent of where he looks, so pressing W, for instance, always moves you the direction that you are facing.

3. I want to eliminate the "ice-skating" effect. On joystick, my character moves flawlessly, but with keyboard, the character slides around like an ice-skater. It's wierd.

On the plus side, collision works...beyond that, I'm lost.

This is what I have so far: using UnityEngine; using System.Collections;

 public class DungeonPlayerBehaviorScript : MonoBehaviour {
     private const float VELOCITY = .075f;
 
     // Use this for initialization
     void Start () {
         
     }
     
     // Update is called once per frame
     void Update () {
         CharacterController controller = GetComponent<CharacterController>();
         controller.Move(new Vector3(Input.GetAxis ("Horizontal") * VELOCITY, 0, Input.GetAxis ("Vertical") * VELOCITY));
     }
 }