Kidou Tenshi Angelic Layer, Hikaru no Go Recommendations
Main characters are about the same age, both have or get some emotional scarring they need to overcome, both are trying to become good at something new, in effect rising to their challenge. Neither anime neglects the cast of supporting characters, always a good thing.
A complete novice in a game rises to be one of the top players in both shows. The major difference is that in Angelic Layer, it's mostly her innate talent that allows her to succeed. In Hikaru no Go, you get a much better sense of how much hard work matters in the game, and how difficult it is. There's a lot more suspense in Hikaru no Go, too- in Angelic Layer the outcome of the game is easily predictable before it starts.