I had a 5 and went to a 6S. I too had always backed up to iTunes but went with an iCloud backup this time.
Because it was an initial iCloud backup, it took a long time. I plugged the phone in, switched on Wi-Fi, changed the Auto-Lock to never. And waited. And waited some more. I did have to buy some extra iCloud storage though.
Then I started the setup of my 6S, restored from iCloud, clicked on the apps so they would download, and I was all done.