^
For screen capture/recording software, you can try NCH Video Capture (
http://www.nchsoftware.com/capture/index.html) suggested by AYYX and Boblove321. I'm using it myself to record other live streams and it does a good job without the restrictions that come with a lot of other free programs (e.g. max recording time limit, watermarks etc.). The only problems are:
1. You need a computer with fast CPU processing speed and reasonable RAM as there have been cases where the recorded video lags.
2. The file sizes can be freaking huge depending on the video quality you set but I guess you can always compress and edit them with another software.
3. I think you can record videos only in AVI format without the restrictions. Other video file formats have restrictions placed on them and you need to purchase the full program to make use of those features.
You can also try aTube Catcher suggested by george (Click
here for his instructions on how to use it).
The important thing is to test these software well ahead of time to know which one works best for you before you run into complications in the middle of recording the real thing.
For the archived file, you probably can just download it via a browser plug-in without needing to record it using a screen capture program. I'm not sure about this particular case but I have downloaded archived videos of Ustream broadcast using Firefox's Video Downloadhelper add-on.