How can I turn off data when my phone's screen is off and only let data come back on once per hour or so to sync apps? I have been using an app called Doze which turns off data when my phone's screen is off. I'd like to find a way that would turn off data when the screen is off but would turn on data once per hour or so, sync all apps to get new messages, updates, etc, and then turn data back off. Is this possible or do I need to write my own app?

I found having the mobile data off more than doubles battery life.
Android 6.0 (Marshmallow) introduced new OS features called Doze and App Standby to improve battery life. Doze defers data usage to short windows while the Android device is stationary. App Standby reduces the resource usage of applications that you don't use. 

Personally, I found the battery life improvement from Doze to be tremendous. I often take my phone out of my pocket when I am not using it to keep it stationary to take advantage of the doze battery savings.