Recommended to me by Students OBS Studio is a free program that allows primarily for streaming of gaming content. However it much more powerful due to the ability to overlay images (such as logos), text (such as web addresses or twitter ID’s ) and your webcam(s). However where the software really comes into its own is as desktop capture, even allowing you to move elements such as the webcam whilst you are recording but “transitioning” your layout update when you are happy so that your viewer does not need to see you visually tinkering with your setup. No cost, no time limit, no watermark!
The software is not the easiest to initally use, but YouTube comes in handy as the software is extrememly popular (I would stick to video that are recent due to large changes with the software and confusions with OBS Classic). Admittedly this does not work too well on a single monitor as you would have to restrict the capture area to at least half your screen so that you can use the other half of your monitor for the actual OBS software to manipulate your elements, but I cannot see any reasons why you cannot create reasonably short captures without being overwhelmed.
Find it at https://obsproject.com/