Get all the Knuckles pictures in Sonic's room. This will unlock Chao in versus mode.
Beat story mode to make additional characters available.
Complete the game and go back to Sonic's room. The Notebook should be on his table.
Get all the pictures of Tails in Sonic's room to make Big available in versus mode.
Get the last picture of Amy in Sonic's room. This will unlock E-102 Gamma in versus mode.
Get all the pictures of Sonic in Sonic's room to unlock Super Sonic in versus mode.