What desktop mailer is the best match with GMail?

Try Gmail Offline, it just to slow or missing Internet.

Thunderbird since version 3.0 is seamlessly integrated with Gmail.
Gmail labels-native-understands perfectly, displays them as folders.
The opposite is true — when you create folders in Thunderbird automatically creates the corresponding label in Gmail.
Supported and multi-level folder structure — in this case, in Gmail, you create labels in the name with the slash.
In General, a wonderful integration, web interface and mail client initially is now almost the same, especially if you configure mail sending via Gmail's SMTP.
\r
Seen only one nasty bug.
Of course, if you receive a letter it gets in the Inbox and in folders, sootvetstvuyushie labels.
So, when reading the email is marked as read only in the folder where it was opened.
It would be logical if it was marked read in all folders.
However, after restarting Thunderbird, it will be marked as read everywhere that only confirms once again that this is a bug, not a feature.
Tried to upgrade to version 3.1, but this bug is still present.

Thunderbird works fine, but what about labels not sure as I haven't used

Evo isn't it?

Try Zimbra Desktop. He seems quite tightly integrated with gmail.

the third question on the topic of crappy Internet from the same author :)... hmm...
Thunderbird

The problem is not poor connection, it's over there's something broken. I have the awesomest channel now also mail in "basic HTML". Nitsche, be patient, we all sometimes fuck-UPS happen.