Well since this is for WordPress, you probably want PHP.
And with WordPress it comes with some “helper” functions like wp_remote_request so you’d likely use that.
For a website integration you would likely use a “server to server” token also called “client_credentials” Getting OAuth Access Tokens | Twitch Developers
Since this is for WordPress theres a bunch of ways you could do it. so you’d be looking at some WordPress tutorials on how to make API calls, and then slot it into your WordPress site where you think it makes sence, since it could be a plugin or modification to a theme.