Swans are, and have been, one of my favorite bands of all time. I agree that "Soundtracks for the Blind" is the best album (and really a cohesive, start to finish album, as opposed to a collection of songs). Don't overlook the live albums..."Swans are Dead" is an amazing document of the final two tours, "Public Castration is a Good Idea" is a frighteningly intense version of their early, noisy stuff.
Angels of Light are great too (and have put on some of my favorite live shows ever), however, the album NOT to be missed is the Body Lovers' "One of Three". Mostly instrumental, using both fresh recordings and old sounds from the past (longtime Swans fans will recognize a riff or two), it's one of the most intense records I've ever heard.
I agree that "the Burning World" shouldn't be the first...though it was for me. "Goddamn The Sun" is a great song!