Raspberry Pi 1080p Streaming Setup

I want a Raspberry Pi 4 turned into a solid 1080p broadcaster that can push two separate feeds—a live capture of the Pi’s own screen and a Pi Camera feed—to a public streaming service such as YouTube Live or Twitch... (Budget: $250 - $750 USD, Jobs: Bash, C++ Programming, Debian, Linux, Python, Raspberry Pi, System Administration, Video Processing)