The default webcam that we recommend is the Logitech HD Pro C920. It's reasonably priced, reliable, and delivers good quality video. You can find the C920 on Amazon for 60 USD.
If your budget allows, you can upgrade to the Logitech HD Pro C910. It will deliver a higher-quality video and perform better in low-light. You can find the C910 on Amazon for 170 USD.
You don't have to use a traditional webcam (or built-in laptop cam) to stream live to your website, however. You can also use an Android or iOS mobile phone or tablet, or a traditional camcorder. Click here for setup instructions for these other options.
Mobile phone pros: The video quality from the latest mobile phones is now better than most high-quality webcams, and there are lots of affordable accessories to improve the video and audio quality. Click here to see our mobile gear guide.
Mobile phone cons: Expensive (if you don't already have one). Can't properly use the phone for other tasks while streaming.
Camcorder pros: The sky is the limit in terms of quality. The only restriction is your budget.
Camcorder cons: A good quality camcorder can be high. Requires an additional external encoding device which costs around 700 USD. We recommend the Teradek VidiU.