In Lesson 2 there is a session on typefaces which lives at this address

The Lesson asks us to critique the page itself, so here goes, albeit not very thorough.

This isn't the world's liveliest looking web page but there's a lot to be said for a plain design. However I could have done without the background image. It didn't make the text harder to read, necessarily, but it was distracting. I also found the default text size a little small.

If readability is to be improved I would suggest wider margins either side, maybe putting all of the text into a centre-aligned table set at 90% width. That way there would be 5% white space either margin and it would make the lines shorter. Bumping up the text size by one magnitude might not hurt either. Similarly, more generous line spacing might render the text a little less "monolithic".

I was very surprised to see the two links to external websites were presented in a text only format, i.e. not as hyperlinks.

These were they:

http://www.lonelyplanet.com/

This uses a san serif font with some headings at roughly double the size and others in a smaller font using block capitals. The styling used for links means that they are not delineated except by colour though they appear underlined when you hover over them. The main menu is in block capitals. On the whole the site has a relaxed and uncluttered look and though the text is small it is readable because it's well spaced out. I don't much like the shouty capital letters though.

http://www.microsoft.com/typography/default.mspx

This has a businesslike look to it with the body text mainly in a serif font. However the side menu is sans serif as are some headings - I don't think the mixture works terribly well, it looks like two different web pages in frames (with no borders).
The subheadings are in italics which look rather odd while links are a rather vivid red. But on the whole no better or worse than the other one.

Personally I would recommend against specifying fontfaces in a web page simply because you can't guarantee your user will have it on their system. Relative sizes are fairly predictable and so are colours... so long as you stick to the web-safe palette.