The $130 box gives you a controller and a Chromecast Ultra. You can use both of the outside of Stadia.
They are also optional: you'll be able to play on Stadia without the controller and without the Chromecast (e.g. on a computer with mouse and keyboard).
I don't have prior experience with controllers, and I don't know what is standard. But I can play my steam games with the Stadia controller and use it with https://html5gamepad.com/ (on Windows).
They are also optional: you'll be able to play on Stadia without the controller and without the Chromecast (e.g. on a computer with mouse and keyboard).