This is a very good first project idea because while it does start out fairly simple and with minimum hardware, you can evolve and make it a lot more complex as your skill and confidence improves.
Another idea for expanding it eventually could be a scorekeeper with 7-segment LEDs, but for now just get the basics working.
One project I'm working on now is similar to what you're doing but I'm making it wireless using the six remote controls from a "Remote Possibilities" game.