The majority of the soundtrack is up on that site. On the "Enter the Site" page, you can hear the whole of the "Ballad" instrumental that they're using as an Overture. Once you're in the site, you can hear large chunks of most of the songs, including all of "A Little Priest" (but they're clearly the soundtrack versions of the cues, since they omit any of the dialogue moments).
I genuinely like the whole cast, singing and otherwise. That's not to say that everybody has a good or great singing voice. Often, it's the opposite. But they still work for the character and make their songs compelling, regardless of vocal talents.
I'm especially fond of HBC's Mrs. Lovett. Not a good voice, per se, but she has a fascinating sound and successfully reinterprets the character. No wonder she was Sondheim's favorite.