Stadia is due to launch in November, 2019. The pricing will be $9.99/mo, which will include some games. Other games will be purchased individually, presumably at price points similar to Xbox and PlayStation.
In the future, you won’t need any additional hardware to be able to play; your existing computer or phone will do the job. At launch, however, you’ll need to purchase the “Stadia Founder’s Edition” bundle to get started. This will include a Stadia Controller, a Chromecast Ultra, three months of Stadia Pro, three more months of Stadia Pro to give to a friend, and a Founder’s Stadia Name. The cost is $129 and can be pre-ordered from Google here.