I've only done this for friends occasionally, but my best recollections are only the buddy list and possibly the current mail are saved on AOLs server and everything else you need to backup up.
Your buddy list is stored on the AOL server, you do not need to back that up. I'm not sure you could if you wanted to.
Your address book will have a "backup" or "export" feature somewhere that will let you save it as a file. Then when you're done, go back and import it with the same process.
Your favorites list should have the same feature.
Your personal filing cabinet (PFC) can also be saved as a file. When I've done this for other people, I've always made three files (saved mail, sent mail, and downloaded files). I don't remember if that was out of necessity or convenience. While this saves things for reference as copies, I've never figured out how to put them back into AOL exactly like they were before (though that may just be me, and perhaps there's a way).
More info here
I
think that the current AOL mail is saved on the server also, but don't quote me on that. If you aren't sure, save it into your personal filing cabnet before you back that up.
This information should be buried in the AOL Help section somewhere.