AMD BC250

And it's true that the BC250 card has more drawbacks than a regular PC :(

I've also heard the bc250 uses a ton of power at idle

The BC250 is cool and fun, but it was cool and fun when it was a cheap way to tinker. With a price of 275 europe dollars, you're way better off with that 5600x machine.

The BC-250 is something for fun, but at current prices, is not worth it. It has 16GB of unified memory which is pretty thrift, even if the firmware that allows for dynamic allocation works. That is just not a lot of memory to go around for VRAM, CPU, and system resources, even on Linux. It certainly isn't 'affordable' or a 'bargain' at $200 dollars for what it is. Complications around cooling also make it really bad. The heatsink is designed for low thermal operation and dissipation. You can't really just slap a big fan on this heatsink, and expect it will have higher thermal dissipation. So, the heatsink is a real problem. To properly cool, you need to make a blower style shell, rather than mount fans on top of the heatsink. It's a fun thing to tinker with, and I intend to make a blower style enclosure for one, but it really isn't a 'good gaming PC on a budget' at 200+ dollars and 16GB unified RAM. It's a fun thing to tinker with, that will cost you an additional 100-300+ dollars to optimize.