Interaction Between Core Logic and GameObjects: A n00b's Architecture Problems

I'm new to Unity and wetting my feet with a Backgammon clone. Currently, I have 3 scripts created to handle game stuff:

1. I have my core game logic, GameController set up in a C# script as a singleton. This script takes care of instancing my prefab pieces and governing whether or not a move is allowed.
2. I also have another js script which handles registering mouse clicks on the board mesh, via raycasting, tied to my camera.
3. And another js click script on the prefabs which cause the prefabs to change appearance while selected.

However, I'm struggling to tie this all together. When I click on a piece, I want to communicate that to my GameController, so it can calculate possible moves. Then when I click on a possible move the selected piece needs to move to its new location.

I imagine that there's something horribly wrong with the way I'm going about trying to architect this, but I'm going to blame that on my unity n00b-ness. Let me know if you think you need some code examples, but as this is more of a general architecture question, I'm not sure you will.

Thanks all!