I'm partial to Airmail (http://airmailapp.com/), which I use for a mix of Gmail and self-hosted (IMAP) addresses. Works great, lightning-fast to use, and with a very Mac-native feel.
I've liked Airmail, but it has a tendency towards weird bugs (e.g. adding gibberish attachments to email chains in large numbers). Email tools, imho, need to be 'boring', stable, and predictable, and Airmail never has been, any of the times I've tried to use it.
Does that store mail on their servers at all? It's becoming increasingly confusing as to which of these new mail clients require a 3rd party server for them to do their "magic" on.
I don't believe Airmail requires any 3rd party server. I have been using Airmail for a few years now and really like it.
No. It does OAuth with GMail, but it's a local client.
I have to dissent unfortunately, I find it slow, buggy, unwieldy, and it will frequently do crazy things to HTML formatted emails.