How to back up my iPhone to transfer photos and contacts?

I had a 5c and just bought an 8. The problem is that my 5c I used my dad's apple account and with the 8 I will be making my own so I can't use iCloud. I have never backed up my phone (yeah, that one alert you get every week to back up your iPhone? I was easily over 150 weeks…) so how do I do it? I have a Mac. Also, I want to transfer over everything EXCEPT music. Is there a way to choose what I transfer to the 8 or do I have to transfer everything over and then delete the music? Its 10 gb I just want it to stay on my 5c, its my dad's music and I have my own Spotify I will use on the 8.

Any useful tutorial videos on YT or guides to help me?

ICloud