You should set up the iPhone with the Apple ID that you want to use, for iCloud and the iTunes and App Store.
By using the Apple Music subscription through Verizon, you get a subscription on your account with Verizon, not on your Apple ID account with Apple. In order to use the service, you need to link your Verizon account (phone number) to your Apple ID.
About bundling Apple Music through mobile phone service providers - Apple Support
Link your Apple ID and mobile number
Go to applemusic.com/carrier on your mobile device to verify your subscription and link your Apple ID.
Changing accounts does complicate it, as possibly neither organization has provisions for that.
Also note that using iCloud Music Library on your iPhone, makes it an “associated device”, which may limit how often the device can be registered with a different Apple ID account for such a service.
View your associated devices - Apple Support
When you try to associate another Apple ID with a device that was already associated, you might see a message that says, "This device is associated with another Apple ID. You cannot associate this device with another Apple ID for [number] days." Depending on when you associated your device with your Apple ID, you might need to wait up to 90 days to associate the device with another Apple ID.
