Do you want the cheapest option?
There are so many!
If you have an Android phone you can install the Steam app, and get a Steam controller, link the steam controller to your phone over bluetooth via the Bluetooth update for steam controller, then connect the android phone to the same WiFi network as the PC with PSOBB installed and Steam, you will be able to stream PSOBB from the PC to your Android phone and connect the Android phone to your TV via HDMI cable assuming your android phone is compatible.
This should work on Samsung high end phones no issue or equivalent with HDMI support and Bluetooth.
Here is example set up: using a Samsung Galaxy Note 8, and this adapter, you can plug the Galaxy Note 8 into ethernet wired home network for max performance and your TV via HDMI. Your phone can also be charged when plugged into this unit.
https://www.amazon.com/dp/B0794WTTL...f60208201ad02c1973b97048be8dd5&language=en_US
If you dont want the wired home ethernet feature just get a cheaper unit with HDMI only, and try to get a cable that charges the phone when connected.
Here is an article on how to link a $50 steam controller to your phone where it will run any game remotely from your PC:
https://support.steampowered.com/kb_article.php?ref=7728-QESJ-4420
Steam Controller and Steam link :
https://store.steampowered.com/app/353370/Steam_Controller/
Total cost: 90 bucks if you have a galaxy 8 or newer for the above solution to work flawlessly using the USB C port on your phone. Etc. Also the above Dex unit might even allow you to hook up USB controllers like xbox one, PS4, or steam controller. However I recommend the steam controller myself.
Another option is to get a steam controller, and Steam Link, which will stream PSOBB from your PC to the Steam Box over a wired or wireless network.
Basically option 1 and 2 are like remote desktop options. They are functionally the same just one uses android phone as the steam link, the second uses a dedicated steam link box. Both options stream the game at 1080p or lower.
Alternatively just get a media center, laptop, or any kind of computer which has a displayport, DVI, or HDMI output and connect directly to the TV. The better the specs, GPU, etc the higher the resolution you can run PSOBB, ie upto 4K with a Radeon 390X or above.
What I personally do is hook my laptop up with HDMI to my TV, then use my steam controller with wireless dongle to play for best performance.