Since my initial reply, Apple's released its Apple Music support site.
https://www.apple.com/support/music/
You're sharing an iTunes Store account - what you do with your iCloud accounts has nothing to do with your business relationship with iTunes. [Yes, you'd setup Family Sharing by accessing iCloud settings, not iTunes Store... I'm sure they had their reasons - probably that, as time goes by, there will be more Family Sharing features that rely on iCloud (there's already the shared calendar and photo album, I suspect we'll eventually see a shared photo library, shared contacts....)]
Here are some key points: With an Apple Music individual membership, only one device/computer can stream Apple Music at a time (if music is downloaded to the device, it can be played, however). As you've already learned, all the devices signed into that individual account will show the same library, playlists, etc.
With a Family membership, each family member can stream at the same time, and each family member's library will be independent of the others (iTunes Store purchases made with one account will still be shared with all). Since you already have separate iCloud accounts... I'd say, spend the extra $5/month.