Serif fonts are traditional and classic. They are recognizable by the "serif" at the ends of most letters.
Sans serif fonts are more modern. They can be both professional and cutting edge. They have no "serifs."
Monospaced fonts allow the same distance for each letter. These are harder to read, and therefore, should only be used for decorative purposes.
Cursive fonts are only for decorative purposes, not body text. Many are low in readability, despite being attractive, so be sure to evaluate that the text can be very easily read. Some very readable fonts may be acceptable as headers.