You're pretty save with Helvetica/Arial (yes, I know there's a difference!) or Verdana for sans-serif or Georgia or Times for serif. In your css you can just put a list in your preferred order. You should always end in a generic font-family to cover all your bases.
My sites usually look something like this:
font-family: Helvetica, Arial, sans-serif;
font-family: Georgia, serif;
If you want to get cute and fancy with your typography, you should look into SIFR, which uses flash to embed special fonts.
