Forget all those other games.
Go is truly the game that takes "minutes to learn, but a lifetime to master." The rules are very simple, but lead to a wealth of complex situations and possibilities. Unlike Chess, which even at the beginning has a highly limited number of potential games (10^50 or so), Go begins with an empty world and opens it up to a vast array of potential development (10^250 or so).
The rules are very simple and can be explained to children.
The lifetime to master part takes place after you have a good grasp of the rules and start trying to see common patterns and behaviors and their consequences.
Because of this, computers, which have managed to conquer chess, are still struggling against Go. The best computer Go player I am aware of is still ranked as a fair amateur, and most that are available for common use are ranked as middling or poor amateurs.
If you are interested in learning, there are a small number of books available. You can get a start with the Rules Node. Also, Go is available on the Internet.