Use one Apple ID for Apple Music and another for iTunes & App Store

There are a couple of gotchas I'm aware of.

1. If you buy apps on both iTunes accounts, they all get listed together when updates become available, not just the ones on the account you're currently signed into. So if you click 'download all free updates' iTunes will only download the updates for the account which is signed in. This can be confusing because you've told it to download all free updates and it doesn't tell you why it hasn't downloaded the others.
2. If you have an Apple TV and you want to use Home Sharing, then you can only share the content for one account at a time.

You can use a shared Apple ID for the iTunes, and app store purchases. Yes, you can select which apps sync to different devices

To sync downloaded apps to iPod touch, iPhone, or iPad: Connect your iPod touch, iPhone, or iPad to your computer.

In iTunes, select your device (below Devices), and then click the Apps button.

Select Sync Apps, and then select the apps you want to sync.

You can create a unique Apple ID to use that for syncing contacts and calendars via iCloud. You can also sync contacts and calendars from an Exchange Server (or Google). Assuming you don't share your Mac account across the entire family, you can also just opt to sync contacts and calendars locally.

You may find the Macworld article All about iCloud: Common signup scenarios to be useful.