TerriblePurpose: I just checked it out after reading your post. Looking at the 'About Stadia' tab, it shows they currently only have the Stadia Pro subscription available currently for (in Canada) $11.99 a month. Pro includes resolution up to 4K, 60FPS, and 5.1 Surround Sound. You do have to buy games, but there are also free games 'released regularly', and you get Pro-exclusive discounts on 'select game purchases'
Coming next year is Stadia Base which is free and gives you resolution up to 1080p, 60 FPS, and Stereo sound. You must buy games, but don't get access to the free games and no discounts.
A tad ironic that the 'free' games are only available if you're
paying for a subscription. Not so free after all...
Neither the Pro sub nor the free Base are actually available to get standalone right now. Currently the only way to use Stadia is to buy the Premium edition which includes 3 months Pro sub, the controller and a Chromecast Ultra (to connect to a TV).
On the chromecast you can only play with the controller right now I think but on PC you can use most common controllers or mouse/keyboard, assuming the game supports it.