Oh boy, what a great question... I could ramble about this so much it'd crash this forum's server. I'll keep it simple.

A room with awesome movie posters and cool stuff we like all around us. It'd be acoustically treated of course with sound panels.

We'd have five Rode Procasters, or similar dynamic mics mounted on scissor arms and running to a Presonus StudioLive 16.4.2. That would feed into a desktop PC which would probably have a Blackmagic Designs ATEM Studio Switcher added to it. Feeding that would be an HD camera locked down on a wide shot since we're an animated bunch. That PC would take care of all streaming.

I'd have a laptop on the other side that would feed the ATEM video of its screen (chat room, pics, videos or whatever we're talking about at that moment). There might also be a couple of bargain laptops off to one side that would feed in Skype guests (we rarely have them though).

And of course, there'd be a mini-fridge stocked with our hosts favorite beers and sodas.