Under 200, there is n100 firewalls mini pc. It has quicksync so easy to transcode, and cpu is 6w tdp. Whole pc on idle consumes 11w and max load 22 to 28 w, depending on a
How many lan ports are being used. U can check aliexpress and amazon for it. There's is also n305, which has 8core, but cpu is 15w tdp and will max consume 35 to 40w. This will cost more than 300usd.
Check servethehome youtube videos on it. He tests them in detail.