I have used Twitch in my personal life, and I have used YouTube with work.
Both are incredibly easy to setup and work with though. Twitch is arguably more popular though, and it has the option of directly exporting to YouTube. YouTube Gaming is nice because if you have a gmail account, you already have a YouTube account. While I am sure that there are other options out there, these are the best for what you are trying to accomplish, and I can personally vouch for both platforms. Your 2 options are YouTube Gaming or Twitch. For my recommendations, I will assume that you simply want to get a stream up and running, and after that we can talk about what you can do to make the stream more appealing. Do you simply want to stream the game from a fixed position camera and that be it? Or do you want to include additional elements to the stream? If you are relatively new to videography, it can be easier to simply start small and do a basic stream. The first thing you need to do is establish the scope of what you want to accomplish. Once you overcome the hurdle of getting everything set up, it's a lot easier. Streaming is really fun, but it can get complex relatively quickly depending on what you want to do.
