I have a document around here somewhere explaining how I process mail. I’ll track it down. I’ve been doing inbox zero for about a decade now, it works pretty well. Let me warn ya about those stragglers though: move them out. Externalize your todo, and move the mail out of your inbox. You can easily find it when you are ready to reply.
This should not make sense, but it will. Those little “presents” clog up the pipes, and draw your attention to an inbox you likely have auto-refreshing. At the very least don’t auto-refresh.
I check mail on a single device, with mutt, and inbox zero each time I launch, which is twice a day (barring some dumb automated message I need to check).
I don’t know if I recommend it, but I really enjoy #taskwarrior for todo items. 
Also, we have an exploration quest for inbox zero: Explore inbox zero