How do I move pictures,music,contacts etc from 5c to a 6s
Assuming you have a paid iCloud subscription that allowed you enough storage space to backup everything, yes, you can just login to your iCloud on the 6s and restore the backup. If you do not have a paid iCloud account, chances are you don't have enough space (free plan is 5GB) and you will need to do a local backup to a computer using iTunes, then restore also using iTunes. 

Contacts are not typically stored on the SIM anymore. It's more so just for cell provider activation and service.