If I switch to Apple Music through Apple do I lose my music?
You get to keep your same iCloud Music Library and playlists, as these are linked to your Apple ID. Even if you are unsubscribed for a few days in between, the you would still get the Library back.
I’d like to enroll in the family plan they offer. How does it work? Payment is collected how?
You cancel the subscription with Verizon. You define the family group, by setting up Family Sharing, with Apple IDs for each group member. You sign up for the Apple Music Family subscription. Payment is done by the payment method that you have set up for your Apple ID for iTunes Store and App Store purchases. The Family Sharing organizer will need a payment method that allows for automatic pre-authorized billing (e.g. credit card). Billing is done monthly, on the same day of the month as when the subscription started. The other group members do not subscribe themselves, but get access to the service by being part of the group. The other group members get to have their own individual iCloud Music Library and playlists.
Family Sharing - Apple Support
Set up Family Sharing - Apple Support
Get an Apple Music Family subscription - Apple Support
Payment methods that you can use with your Apple ID - Apple Support
Change, add, or remove Apple ID payment methods - Apple Support