If you want a zero inbox client, then InBox on top of gmail is pretty good.

I use FastMail as my primary email, and I don't quite do zero inbox. I probably have on average 5 to 8 emails in my inbox, and a few stick around for days.

It takes some effort and overhead but I am trying to move away from email as being a "memory box" for organizing my life. Instead I am using subject organized markdown files stored in encrypted cloud storage where I maintain tasks, research notes, etc. since these are synced on my laptops, I can search them with spotlight, cortana, etc.

Combined with FastMail, this scheme keeps me organized. As easy as using InBox for email and TODOs? No, but so far it is working for me.

Spark is great for this; it supports IMAP very well. You can customize the UI for archive, trash, snooze and pin swipes to your liking. And unlike Mailbox, does not rely on server side access to your email or email account.