1 Webcam software
You want to record a video of your face?
Simple, reliable software choice: Cheese whose unremarkable feature is just that it works. Takes photos and videos with minimal fuss AFAICT.
A fancier alternative is webcamoid which has many filters, features, virtual webcam devices, and inter-application routing. However, for me it records only silent videos, which is a showstopper for recording lectures.
2 Linux-compatible webcams
A good first approximation to “which webcams are Linux-compatible” is the Linux UVC lists. Confusingly, the recommended webcam app for Ubuntu, Cheese never works for me, which might persuade me my webcams don’t work. But they work in everything else. A good alternative “pro” test app is guvcview which additionally has extra diagnostics.