I’m actually working on an article about this. There is no good simple answer to your question. It’s a matter of taste, readability, and effect. I prefer a strong serif font for my heading (say, the Palatinos), and a classy, thin sans-serif for my text (say Frutiger or Helvetica Neue), but that’s strictly a matter of personal style and desired effect. The Web standard used to be the reverse: sans-serif headlines and serif text. Basically, you need to create a strong “font stack” to appeal to the widest possible audience: begin with the font that you like the best, then following with more widespread alternatives and finishing with the generic serif or sans-serif (or monospace, or cursive, or whatever).
Some people advise you just stating serif or sans, and letting the user’s default settings come into play, but I don’t agree.