What capture card are you using? Let's address that first. Built-in, or usb 2.0/3.0? Are you using Windows, Linux, or Mac?
Newscasting headphones have solid built-in microphones. Sennheiser, Beyerdynamic, Shure. and Audio Technica make great ones. For reference, Chibo and Gimr use Senn, and AT respectively. I use monitoring headphones with clip-on lapel mics.
You don't need a mixer right away, but it does help. An external DAC to lower the noise floor, and an inexpensive mixer will help with audio and bypass window's inferior kmixer. You really only need an audio splitter if you're using on-board and being cheap about it.
As for software, I personally don't bother with audacity, I use programs that can interweave audio with video natively. We're talking program like Open Broadcast Software, XSplit, VirtualDub, etc. I personally recommend OBS, as it's open source, and extremely strong.
For your commentators, I recommend an external monitor for them, and keep all the chat, etc to yourself. While sometimes it is nice to interract with the stream chat, at higher profile tournaments, it's kinda unprofessional. Give them a monitor with full-screen smash, and have the person running and maintaining the stream handle all of the technical aspects on their own.
Try to put together a solid, dedicated crew of commentators. Everyone and their mother wants to try their hand, but not everyone is cut out for it.
As for links:
Professional Headsets:
Shure:
http://www.amazon.com/Shure-BRH440M-Dual-Sided-Broadcast-Headset/dp/B009K1WTO0/ref=sr_1_15?ie=UTF8&qid=1389221602&sr=8-15&keywords=shure headset
Beyer:
http://www.amazon.com/Beyerdynamic-DT-109-200-50-GREY-Headset-Hypercardioid-Microphone/dp/B003D85G96/ref=sr_1_1?ie=UTF8&qid=1389221789&sr=8-1&keywords=beyerdynamic news headset
Senn:
http://www.amazon.com/Sennheiser-Dual-Sided-Closed-Back-Supercardioid-Microphone/dp/B000Z76JBM/ref=sr_1_4?ie=UTF8&qid=1389221725&sr=8-4&keywords=sennheiser 280 headset
AT:
http://www.amazon.com/Audio-Technica-Broadcast-Stereo-Headset-Dynamic/dp/B003D87JI2/ref=sr_1_2?ie=UTF8&qid=1389221850&sr=8-2&keywords=audio technica headset
http://www.amazon.com/Audio-Technica-ATH-770COM-Stereo-Headset/dp/B003X519CW/ref=sr_1_4?ie=UTF8&qid=1389221850&sr=8-4&keywords=audio technica headset
Open Broadcast Software:
http://obsproject.com/