How to set up my new iPhone on my Mac?

I've recently got my dads iPhone6 and gave my iPhone5 to mum. My old phone was always used on my Mac but now I have this new phone I don't know how to change it to think that's the main phone. Because my mum is using my iCloud accounts, like iTunes. I put in my new (dads accounts) iCloud details on my Mac but still doesn't wanna put music on my phone or that. I hope I explained my problem good enough, I hope someone could help please!

Did you not create a backup of your old phone? Simply plug it in and click restore from backup. If you did an iCloud backup then simply reset all content via the settings app and it will restore it as new so you can enter your Apple details and then restore your content back onto it.