I'm a self-taught, casual graphic designer, but can I add my name to the list of folks who hate Papyrus? I refuse to use that font, and no matter how nice someone's work might be, if I see that font on there, it just screams "newbie" to me. It's one of the few fonts that I can identify by sight, and it sticks out like a sore thumb.
For regular, non-script fonts, I like Georgia and Verdana. I use Verdana on my website (www.spareoom.net) and I like how it looks on the site, so that's good for me.