Ditto. I turned off virtually all notifications on my phone. Only phone calls and text messages get through (which for me is quite rare).

I realized that almost nothing on my phone is important enough to interrupt me whenever.

I just use Priority Mode and put the phone face down if the notification led will distract me.

I too turned off notifications on gmail a long time ago. However, I've setup some filters looking for words like "urgent", "emergency", etc without telling people that I have. They're all labeled accordingly and that specific label makes a noise on my phone. It seems to work pretty good so far.