Software:
Camstudio 2.7 has solved the general audio/video sync issues. However, for me it still gets desync'ed after pausing and unpausing (audio gets 0.3s ahead of image). I reported that. Now there's 2.7.2 that I don't know if it solves that issue or not, because it works wrong in my PC: making a 0 messagebox when starting to record or unpausing and a "1" messagebox when stopping. It's very fast creating the file and it's small. Worth keeping an eye on. To edit, windows video maker is easy enough to figure. Camstudio only records from one audio source: either the system or the microphone.
Another freeware choice is Debut Video Capture Software. Files are only slightly bigger than with Camstudio, it's equally fast creating the file. No waiting half an hour for a 10 min video after stopping like with Camtasia. You end and you have the file. They also have an easy enough to work with editor called Videopad Video Editor, also free. These two will "nag" you telling it's not for commercial purpose when you run them, but it shouldn't be a big issue. The issue with Debut Video Capture is that when you pause and end, it eats the last second of video, so you have to wait for around a second after saying the last word before pausing/stopping. Debut can capture audio from both system and microphone.
As for Fraps, that will make a stamp with "fraps" at the top of the video, the default settings make a huge file size and I don't know of any way to change that. The program has no way to modify the video it creates, I guess it would be going to the tools to edit options for the codecs it uses.