This is a tough one! Professional game streaming is an emerging field and there is a lot of art in their craft (beside being quite good at gaming.) I have streamed before, but am not a professional streaming gamer, so take this with a grain of salt!
The equipment could be as simple or as expensive and complicated as you like, but it all would depend on what kind of show you're putting on. The reason I say "show" is that you'll be competing with other people in order to capture viewers for a sustained period of time. If you're able to successfully entertain them and predictably bring back a number of viewers to your stream, you may be able to attract sponsors that can help make this lifestyle sustainable for you.
I would suggest - instead of diving for nice equipment first - to spend some time describing for yourself in writing the kind of streaming / show experience you'd really enjoy making, then do a search for a variety of successful professional streamer's "shows" and note what works well for them and examine their differences. After all this, I'd suggest to start *very* simply. Don't ask too much of yourself or over invest in equipment in the beginning.
Twitch has many suggestions for streaming software you can use here. You could start by using any one of those (I use OBS Project) that work for your gaming system and a mic (perhaps an affordable gaming headset) and just get a sense for what it feels like to be playing, streaming, and putting on a show / talking (mostly to yourself or a guest on your show). As you become comfortable with it, and you get a better sense of the kind of streaming experience you want viewers to have, you might reach out to streamers that inspire you to learn about their streaming rigs.
This professional recommends the following next steps:
- Describe, in writing, what you want your streaming experience to be like.
- Examine what you think works, doesn't work, and examine the differences between professional streaming "shows"
- Try out streaming with minimal investment (OBS Project and affordable mic/headset) and see how it feels.
- Reach out to streamers that inspire you and learn about their streaming rigs.