unity – ScreenToWorldPoint: How much depth has to be added to screen point?

I am developing a 3rd Person Controller.

The hero’s chest should be rotated towards a point on the screen.

To determine the point, I use the following code:

var mousePos = Input.mousePosition;
mousePos.z = 10; // Make sure to add some "depth" to the screen point 

var aim = Camera.main.ScreenToWorldPoint(mousePos);

Then I rotate the chest like this:

Vector3 v = new Vector3(0, aim.x, 0);
Chest.Rotate(v);

It does work, but it rotates only minimally, and the the direction is inverted: If the mouse is on the right of the screen, the chest rotates to the left and vice versa.

Also, I’m not sure how to include the model’s overall rotation (but I don’t know yet if that is necessary).

Does anybody have any idea what I’m doing wrong?

Edit:
When I add more depth to it, it rotates much more:

var mousePos = Input.mousePosition;
mousePos.z = 100; // Make sure to add some "depth" to the screen point 

var aim = Camera.main.ScreenToWorldPoint(mousePos);

But I have no idea how much depth is actually needed.
If I add 1000, it rotates like crazy.

So I would like to know how to calculate the amount of depth that should actually be added to the screen point.