Good Gmail desktop mail client for Windows?
The best UI you're going to find is the gmail web UI itself. That's what you're intended to use. Gmail's tagging/labelling system seems to be outside of the imap/pop standards, so I think finding a third party application that correctly supports them, is probably an exercise in futility.
Support for multiple Gmail accounts
You wanted multiple gmail accounts supported - a way of doing that is to enable "multiple sign-in". This feature lets you click on the email address (account) you're viewing in the upper corner, and select other accounts you're signed in to. Thus letting you switch between mutiple accounts. Here's instructions on how to enable this.
Mail cached locally, a desktop client should have a well working offline mode
I believe this too is in fact supported from the web ui. Take a look at Gmail offline here.
Support for Gmails threaded conversations
Check.
Support for Gmails labels (tagging) system
Check.
Integrates with Gmails spam filtering (mark as spam, mark as genuine email)
Check.
Integrates with Gmails contacts
Check.
Lightweight, fast to load, uncluttered user interface
I've found the gmail ui to be reasonably heavy. You may want to experiment with using it under different browsers. The main potential benefit is that different browsers can use different javascript engines. I believe the next Firefox release is meant to have a far more efficient javascript engine. I'd guess that Google Chrome is pretty darn efficient for gmail. In the worst case, you could opt to run gmail in HTML only view - that'd be light-weight.
Edit - Thunderbird?
As an alternative, I suppose Mozilla Thunderbird looks like it may fit, IF you install certain addons.
For conversations, try this.
For contacts, try this.
Though, I think you'll still find the label support to be weird. I think you'll get label support at all, if and only if you set up gmail access over imap (and not pop).