There are several type categories: Script, Serif and Sans Serif are the most common. Each comes in thousands of variations depending on the type foundry that created it.
Scripts are more like handwriting. You can find delicate curves and curls on the ends of letters for an elegant flow of text, or unpredictable letter endings that feel more like actual handwriting. Scripts can be used for businesses like wedding planners, some types of restaurants, and more elegant business types in general. Some examples of scripts are: Edwardian Script, Brush Script, or Mistral to name a few. The downside to using a script is it is harder to read so use them for sparingly.
A Serif is also considered to be an elegant type form and usually easier to read than a script. A serif is the little tiny leg that hangs off the end of a letter. Some examples of a serif are: Times Roman, Garamond and Lucida Bright. For some uses the little tiny Serif seems to flow the letters together smoothly which makes it read easier and there are cases when the little tiny Serif gets lost which makes the design look fuzzy and unprofessional. Be aware of the possible challenges, and if you are set on using a serif then experiment with different types of serif fonts to find the best readability.
Sans Serif means Not Serif, so that means it is a style that does not have the little leg or Serif on the end of the letters. Some examples of Sans Serif fonts are: Helvetica, Arial and Impact. This type is considered easy to read since there are no little parts hanging off the text; it is very clean and bold in appearance. Use really depends on the right feel for your project
Whichever type style you choose experiment with different fonts to get the right feelings and readability for your creative project.**Check out great tidbits like this one my book "Your New Business Logo". Just clicke the ebook link for more information.**