Using an iframe is correct. The html id does not matter, accept for your own needs, such as styling or javascript interaction. You can set the size using css. The only important thing is the url you use. In the following sample you can change the width and height to fit your needs. All that needs changing is the Twitch username. Just set it to your name and it will load your chat.
<iframe style="width: 300px; height: 500px;" src="http://twitch.tv/YOUR_TWITCH_NAME_HERE/chat?popout="></iframe>