If you are new to fonts, take a quick look at this font exploration module Dr. Carrie Heeter created for her Flash Design students. In particular, note the main difference between the serif and sans serif fonts.
Serif fonts (short lines and decorations stemming from the ends of letters) like Times New Roman are more readable in print because the decorations help the letters flow, whereas sans serif fonts (without those decorations) are more readable on screens due to the limitations of computer monitors. Arial and Helvetica are common fonts with excellent readability on screen. Verdana has been designed specially for on-screen readability on various operating systems, especially at the normal size range of 10 point through 14 point.
- Compare a common san-serif, serif and mono-spaced font. Notice how the serif font (Times New Roman) becomes more legible as it increases in size, while the sans-serif font (Verdana) is legible at a smaller size.
If you need to to present a table in which all the numbers line up vertically, use a mono-spaced/fixed-width font (each letter occupies a fixed-width). Courier New is a common mono-spaced font.
Unless the style of the font is of key importance to your material, limit your fonts to those which are commonly available on different systems. If a required font is not available, your reader's browser will substitute it with a default font, usually Times, Arial or Helvetica. Using common fonts will also make it simpler for users to adjust the font sizes to their preferences, especially those who are visually impaired. Here are the default fonts on Windows and Mac OS.
For a detailed analysis of commonly used web fonts, see an article on How should text be presented within a website?