The way that character autopgraphs work are that during meet-and-greets or character meals with the characters, they will write their signiture in your book. You don't need a specific one for each park. You don't even need one of the official ones they sell in the park. You can use a notepad, journal, album, etc. You can feel free to be creative as possible. Some people even get hats and shirts signed. I like the official one becuase it's just big enough for a signiture, but small enough to transport easily. You do need to supply your own pen as well. Fatter pens work best since they are easier for the characters to grasp with their paws and gloves.
Just one more thing- not all characters sign autographs. Buzz, Woody, and Mr. and Mrs. Incredible use ink stamps to sign while other characters like King Louie, Mike, Sully, and Figment are physically unable to sign autographs. I belive
http://www.wdwautographs.com will be able to tell you what characters sign or not, along with any other info I've forgotten.