AmazonBasics Lightweight Mini Tripod https://www.amazon.com/dp/B00M78G2VO/ref=cm_sw_r_cp_apa_aE5izbC8YQG5Q And https://www.amazon.com/dp/B01L3B5PBI/ref=cm_sw_r_cp_apa_ME5izb5G5HJEA Are what I use, it's a tabletop tripod, but you could probably get a full sized one with the mount for around 20
I think this is it:
Which tripod is the cheapest and works? Would this be fine Amazon Basics Lightweight Mini Tripod https://www.amazon.com/dp/B00M78G2VO/ref=cm_sw_r_cp_api_glt_fabc_EAG82EC4XBPRDVSXXNPA
I got the Logitech C615 ($70 - $75). It works.
It meets the specs, but I had a little trouble with it. The cord is too short, so the vertical field of view is a bit too small. I had to take my first proctored exam hunched over a little so the proctor could see my hands and my entire face at the same time. I added an extension USB cable and it works great now.
Here's the USB extension I used ($7). https://www.amazon.com/gp/product/B019E0FB4G
And the tripod ($11). https://www.amazon.com/gp/product/B00M78G2VO
I'm sure there are cheaper solutions, but I know this set up works.