One of my favourite features in iOS 10 is the new mail filter option within Mail.app
My default view now is to only see unread and flagged, I do this as follows
- Tap Mail
- Tap All Inboxes
- Tap the circle with three lines inside it in the bottom left corner
This will then apply a filer, which you can tweak by tapping Filtered by: that now appears at the bottom on the mail app. Within here you can now change what appears for me I have Unread and Flagged.