Kind of a two step operation IMO.
1- to transfer your music connect a cable to your galaxy locate the folders that your pictures and music are in.
2- create a file on a pc or Mac for your pictures
3- put your music files on iTunes.
4- sync your iohone with iTunes. As long as you select the correct files in iTunes your music and pictures will sync over.
As for your contacts, create an email address in Gmail. When you set up the account in gmail make sure you select " sync contacts with gmail. In order for this to work you must import your contacts first into gmail on a pc or Mac. Another way would be to create an icloud account and import your contacts into icloud on a pc or Mac and it will sync with your new iPhone.