Good practice for storing layerInt values

Personally I believe it depends on how frequently each layer is being used. If I know only one type of object in my scene is to be drawn on a given layer, then I would handle the layer in that MonoBehaviour only.

 public class MyInvisibleObject : MonoBehaviour
 {
      private const int detectiveVisionLayer = 10;
 }

However, if I have layers that are used by many objects, I would keep them in a static class somewhere:

 public static class GraphicsConstants
 {
     public const int fooLayer = 1;
     public const int barLayer = 2;
 }

Of course, you could do this in a List or Dictionary instead.

Now, I avoid using strings as much as possible, but with layers I prefer to use strings because it's easier to see where the result in the scene is coming from. As such, I tend to use this method a lot in my MonoBehaviour subclass:

 // Convenience accessor for getting/setting layer by name
 public string layerName
 {
     get
     {
         return LayerMask.LayerToName(this.gameObject.layer);
     }
     set
     {
         this.gameObject.layer = LayerMask.NameToLayer(value);
     }
 }