In this combination i'd say evolution, but i do not know the kde universe too well.

kontact/kmail (KDE mail ua) used to integrate all that stuff the only thing it lacked was an ability to handle HTML email. At the time the developers kept insisting that email should all be plaintext and they weren't going to allow HTML mailing in kmail.

I moved to thunderbird.

The rest of KDE4 caught up to being release standard at about version 4.6 and Kontact looks good but I've become entrenched with TB now.

gmail/google calendar/google contacts. I've been a desktop Linux user for 14 years, and while Evolution worked well enough for a while, it really stagnated about 8 years ago as all the users switched to webmail. I tell chrome to pretend it's on Windows and use Outlook Web Access when I need to interact with Exchange, and I actually like that better than outlook on windows anyway, but nothing beats gmail.

I'm using Evolution on imap now and it sucks. I'd been using mutt for many years and decided it was time to try a GUI client now that most emails are fairly graphical.

Evolution will routinely chew on my disk for over thirty seconds before starting up, for no clear reason. It pops up strange error messages about host resolution when I know the host is up just fine and quite reachable. It doesn't atomically handle email moves, so I've closed the client and later reopened it to find messages I've moved right back in their original places.

I honestly don't know. I've tried Zimbra and Thunderbird and some other client I can't remember the name of, but in general even Thunderbird isn't great - I usually resort to webmail.

Thunderbird+Lightning (for calendar and contacts). Or Claws mail for a "pro" (rough but very fast and functional) solution.