If your old machine has Firewire ports, use Firewire target disk mode. Power down the old machine, and restart it while holding down the "T" key. Then connect a Firewire cable between it and your iBook, and it will appear as a hard drive on the iBook. Drag and drop the files you want to copy, and then eject the old machine's hard drive.
Programs like Mail and iTunes store their preferences in the Library folder inside your user folder. Once you've created a user account on the iBook, you could just drag over all of the contents of your old user account to the new one, overwriting the Library, Music, Pictures, and other folders. If you log out and log back in, your new Mac will have all the same settings as the old one. One exception is network settings; they are not stored in the user account so you'll need to recreate them.