You don not need an Apple Music subscription to share purchases.
Apple Music is a streaming service and if you decide that you want to subscribe to it, you will need a Family Apple Music subscription rather than an Individual Apple Music subscription -- but, again, that is only needed for Apple Music streaming and has nothing to do with sharing purchase.
For more information on sharing purchases, see: How to share purchases with your family - Apple Support
To make purchases without an Apple Music subscription (and with or without Family Sharing), see: Buy music from the iTunes Store - Apple Support