My crontab (https://github.com/NateEag/dotfiles/blob/master/lib/.crontab) runs a check-mail script (https://github.com/NateEag/dotfiles/blob/master/bin/check-ma...) every five minutes.
The check-mail script is just a wrapper around mbsync (http://isync.sourceforge.net) that invokes 'notmuch new' after running, so notmuch can index and process new messages.
My notmuch post-new hook does a bunch of tagging for me, so I have to actually look at as little email as feasible, but the main thing it sounds like you're interested in is the notification setup:
https://github.com/NateEag/dotfiles/blob/858cabd9436d377f8fc...
With that, I can batch-process email a few times a day, while staying responsive to any discussions I actually want to be interrupted for.
The missing piece is reasonable logic for knowing when I should be notified of new threads. I'm currently in a job where people don't expect insta-responses to email, thank God, but I've been in ones where they do and I'd have to think about how to handle that more.
For reading and writing email, I just use notmuch's Emacs modes. You can see most of my interesting config here: https://github.com/NateEag/.emacs.d/blob/75d117befeaaab37cc7...
My one annoyance when reading email is that large inline images aren't auto-resized to fit. They should be, but the Emacs build I use doesn't have ImageMagick support compiled in.
My custom.el probably has some notmuch settings too.
That's the highlights. Hope it was helpful.
With notmuch and mbsync I have the best email setup I ever have. I wish I'd done it years ago.