You can get a first gen Xbox for about $50~$100, including games. Just be aware of the clock capacitor. A lot of xboxes have bad clock capacitors now (they used them instead of coin cell batteries for some reason), which can leak and damage the board. If you get an OG Xbox, make sure you A) check the serial number to figure out where the capacitor is and if the Xbox needs it because B) the last Xbox version had better capacitors that don’t fail nearly as much, but they’re required for the Xbox to start up. On older models you can just snap off the capacitor and call it a day so long as it didn’t leak and corrode the board traces.

Oh, and electron shepherd has an hdmi adapter for the Xbox. Works pretty well.