I'd go with Open Broadcaster Software. It can use both, screen and webcam as a source and even pictures or text.
Here it is, a screenshot of the scene configuration with a monitor and a webcam as source (extra scary).
The usability could probably be improved. Consider some time to get familiar with it and try it intensively before recording or streaming important videos.
There are at least 3 ways of adding things to a scene. To get started, I recommend:
- start the preview
- right click into the preview
- Choose add > something
You can then click on an item and resize it or right click and change the properties.