OBS to stream and record: cost $0 GV-USB2 Capture Card to capture footage from the console: cost $40

That’s all you need. You can add a powered splitter (about $20 -$30) if you want to split the console video and audio so you can play off a TV while you record. Without that you’ll have to play off your captured footage on your computer. There are also cheaper capture card options but they’ll all have worse quality and probably more delay than the gv-usb2.

Here’s the guide I always share for a simplistic streaming setup: https://goo.gl/C78vWx