As everyone before me said, most files will transport just fine. The only exceptions I found when doing this were document files that were saved in native "Apple Works" formating. First save these files to "Rich Text Format" and you will have no problems transporting your documents. I found out the hard way and after I changed over, I had to export all my document files to a relative that was still using a version of Mac OS, have him convert them, and send them back to me.
Edit: I forgot to mention that I simply copied all my files onto a flashdrive (you'll probably need at least 16Gb), and moved them to the appropriate place once plugged into your Linux OS. A little time consuming, but not bad really. Once moved over, check out the backup software (Deja Dup in the repository if not natively installed). If you ever need to restore or clone a new computer you just plug it in, start it, and walk away. An hour or so later everything is installed just the way you had it before. Very cool...