Yes, it's possible. Your family either shares one account or you set up family sharing and keep things separate:
Share purchased content with Family Sharing - Apple Support
Set up Family Sharing - Apple Support
I share one iTunes Store account between 2 macs, 3 phones and 2 iPads. Each device just downloads what apps they need. I set up our household before Family Sharing was a thing.
I would though use multiple iCloud accounts so that you do not share contacts and calendars. Each person should have their own iCloud account but you can share a iTunes store account for app purchases. The iTunes store account will be linked to one credit card, so one of you would take responsibility for paying for everything.