I currently use:
OBS Studio (free broadcasting software with tons of "How To" videos all over the web)
Elgato HD60 (PS4, PS3, Wii U, Switch, Xbox 360, Xbox One, etc recording/streaming)
Elgato HD60 Pro card (has better quality recording options for streaming, literally feels like no latency at all)
AT2020 USB+ Microphone
And plenty of extra HDMI cables, and HDMI splitters.