This is a short video that describes some basic sound setup for doing an asynchronous lecture.
The Microphones I used in the video are ones that I have had for many years. They are not necessarily what I am recommending. They are expensive and require audio interfaces.
A popular choice as a microphone for lectures (and podcasts and other vocal recordings) is the Blue Yeti. It's a high quality microphone in that price range. If you are going to put it on a stand, you will need a stand adapter like the Auphonix Pro Blue Yeti Shock Mount.
Another microphone that is a good choice is the Rode NT-USB Mini. It does come with a stand adapter that will work with a boom stand.
I strongly recommend using a microphone stand rather than placing it on the desk. If purchasing a microphone stand, get one with a boom like the On-Stage MS7701B.