"Heart of Saturday Night" is probably the most accessible album, as Pehare has stated above, though it might not be the most typical. The live, "Nighthawks at the Diner" is my favorite for long car trips.
"Used Songs," "Beautiful Maladies," or another of the composite albums might be a good place to start, as you'll get a feeling for the spectrum of Waits' work.
Also fairly accessible are "Blue Valentine," "Small Change,"and "Closing Time."
If you like his harder-edged stuff, "Swordfishtrombones," "Mule Variations," or "Rain Dogs" are a good listen. If you want to hear him go over the top, try "Bone Machine," or "The Black Rider."
His two newer albums, "Alice," and "Blood Money," are also a middling easy listen. There are others as well that i haven't mentioned.
My personal favorites: "Small Change," "Mule Variations," "Rain Dogs," and "The Black Rider," in no particular order (and subject to change at the drop of a stylus).
