Probably a little late but i have recently made the move to mint and there were several apps i needed. Coming from OSX these were iTunes, iPhoto and Aperture. Aperture was easy Darktable, iPhoto im still working on. iTunes however i sorted out last night. I choose Banshee as the app in the end.
Step 1, Copy you files from your old comp to your new one, ideally on a separate partition or HDD. I changed the name of the folder from 'iTunes' to 'Muisc'
Step 2, Get iTunes to export an XML file.
Step 3, Copy this to your new music folder
Step 4, Do not run the 'import itunes media' as you have changed the location of your music folder, instead open up the xml and do a find and replace. replace you old path with the new path. and click replace all. Should be very easy and self explanatory sounds harder than it is.
Step 5, In Banshee under preferences select your music folder as the source of the music (sorry for being a little vague im on a PC at the moment so am typing from memory)
Step 6, Rename your library.xml file to itunes library .xml (again cant remember exactly but it tells you this at the bottom of the window you have to select it)
Step 7, Run 'Import iTunes Media' from Banshee, this might take awhile.
You should now have all your play lists etc etc even some radio stations i had in an itunes play-list copied over and worked so that was a bonus.
Hope this helps.
I will be documenting how i get on with the move to Mint in other posts or maybe a blog.
Cheers for now