How to sync iPhone to (new) computer and keep everything on the phone saved?

I want to put music onto my iphone (the music is on my laptop, and on itunes).

When I connect my iphone to my laptop it asks me to set it up as a new iPhone.

I cannot risk losing any of my data on the phone (eg. contacts, messages, notes, apps, etc).

The phone is connected to my icloud account, and everything is checked to be saved on icloud.

On the computer there is no option to restore from the icloud account.

Do I restore from the icloud account via my phone (and then will it sync the music onto my phone via computer?)? Or set it up as a new iphone via my laptop?

The end result I need to have is for the phone to remain the same (apps, information, contacts, etc.), except with my music (that is on my laptop) playable in the music app.

Thanks so much in advance for any help that could be given!