I treat it as a secretary. I think of different communication media as having different urgencies / time constants. Emails are a daily report. My phone's notifications are an hourly report. Notifications which I forward to my watch are the instant things. Be sure to mercilessly "mute" most apps from bugging you on your wrist. With this setup, I never feel the urge to check my phone. If there is something important, it would've buzzed my wrist.
Here are my subjectively appreciated apps
Homescreen: Fairweather. It is information dense display of weather, sunset time, pressure, vis., etc.
(Top) Button shortcut: Forecast weather. Shows a probability of precipitation over the next 24hrs (I donated for data from forecast.io). Great for avoiding the rain when walking the dog / biking home / etc.
(Bottom) Button shortcut: A bus/train stop info panel. It uses the phone's GPS to tell you when the next buses/trains are coming. Handy for when there is a stop within 100 feet of the bar and you can know if you want that extra beer or not.
Timer/Multitimer are great. Alarms for waking up are great. 7minute workout app is great.