How I did it:
I already had a Microsoft Exchange email account where my contacts were stored, so once my Windows Phone was connected to Exchange the contacts were there. If you're using anything for email and contacts other than (iCloud or stored on device or simcard), it should be similar. Actually 8.1 has a new iCloud account option but I can't say I have tested it.
For music, there is a Windows Phone desktop app, one of its options for syncing music is to display your iTunes library and let you choose what you want copied to the phone.