Something like this? Arranged by type + year of release. The Pokémon were based on the most popular of the respective type and Gen., based on rankings I could find online (barring Legendaries/Mythicals). I also included a version where one could choose their favorite Pokémon of that type and Gen. instead. They'd have to be updated annually, but that's better than becoming completely irrelevant as soon as Gen. X comes out.
If anyone born before 1996 wants to play, count backward from Normal (Fairy would be 1995, Steel 1994, etc.) and apply whatever Gen. you got involved with the franchise.