Use 1 Apple ID for iTunes purchases of Apps, Music, Movies, etc. and have each family member have a separate Apple ID for iCloud, FaceTime, iMessage, etc. That way you can share app and media purchases without buying the same items more than once and you can each have own identity and backups, etc. for your own devices.
We have probably 8 iOS devices plus a couple Apple TVs that use the same Apple ID for iTunes but each family member has a unique Apple ID used for iCloud. So for example, I use SHARED_APPLE_ID on my iPhone, my iPad, my iPod and on a Mac in iTunes to make purchases and share music, my family members use the same on their devices as well for music and apps. THen I use MY_APPLE_ID on each my own iOS device to be able to use FaceTime, iMessage, iCloud. So I can access the same iMessage account on my phone, iPad and Mac for myself and family members have their own. If I lose or replace a device I can easily restore it with my unique Apple ID and so could any family member, but I am not paying 4 times for the same app we are all using, only paying once.
The only downside is we all share playlists, but you can simply name them for each member or use a unique name or number for each family member to keep playlists separate and individual on each device and just sync the selected playlist for each person to their device.