If it helps, there's also option D: RaspberryPi with Steam Link. Cheap, functional, and flexible.
That's what I set up at home and it's working great. If you play with a controller, note that some games work better than others or have weird requirements to get the controller to work (e.g. for Space Marine 2 I have to keep a wired controller plugged into my main tower for the Steam link wireless controller to work).
RaspPi also gives you the opportunity to set up and play old-school emulated games if that's interesting to you.
No, they're not sold anymore. But the RaspPi acts just like the original hardware once the software is installed and configured. If you like tinkering, it's a nice afternoon project. And since Pis are so versatile, it opens up a bunch of possibilities for other projects (I recommend a PiHole for example) even if this application doesn't fit your needs.