Interesting to hear of a person who wants to start playing GameCube in 2017!
Unfortunately I spent at least 80% of my gaming time on that console with Mario Kart as well as Need for Speed, so I just can't recommend any other game... I used to play "Finding Nemo" for some hours, but that is only fun for kids under the age of 12 I guess. Another alternative would be this adapter to play your old GameBoy games, there I would recommend the already mentioned games of Crash Bandicoot and almost every single Super Mario game!