You'd be best going for "web-friendly" fonts, and its also good practice to create a "font stack" with your preferred font first, and then second and third choice fonts etc, in case a particular person's computer doesn't have your first choice of font.
e.g. "Century Gothic" is a nice "sans-serif" font, so if you wanted to use Century Gothic, then your font stack might look like this:
font-family: "Century Gothic", "Trebuchet MS", "Verdana", "Arial", "Helvetica", sans-serif;
So, your first choice is Century Gothic, but if they haven't got that, use Trebuchet MS, if they haven't got that, then use Verdana, etc... the "sans-serif" entry at the end is telling the browser just to use whatever generic sans-serif font is specified for that particular system if none of the other fonts you have specified are installed.
Likewise, for a serif font, you might have something like...
font-family: "Palatino Linotype", "Century Schoolbook", "Times New Roman", "Times", serif;