i'd say go in order -
gish = loud, raw, beautifully dark and dramatic guitar rock, psychedelic, hyperkinetic, jazzy drums: siva, tristessa, snail
siamese dream = loud, immaculate, beautiful guitar rock. if gish was '60's garage, this is an epic work of pristine, meticulous production - like that overproduced brand of rock from the '70's, but modern songs and methods - cherub rock, geek usa, hummer, mayonnaise
mellon collie = sprawling, exhaustive concept album. wild variation in styles and sounds. this is their 'white album'; schizophrenic, with varying (and frequently - but not always - brilliant) results - jellybelly, 1979, porcelina, muzzle, 33, galapogos, here is no why
adore = goth, synth rock, with shades of olde time americana. they compensated for the absence of jimmy chamberlain (billy corgan's other half) with session drummers (matt cameron...) and drum machines. creative and brooding, frequently challenging - perfect, to sheila, for martha, behold! the night mare
machina I = back to the rock, their most modern sounding record, big guitar anthems, more brooding gothic metal workouts. billy dragged his brand of guitar-based music kicking and screaming into the new century, employing flange and phase and ebow with striking results. i think this album is terribly underrated - stand inside your love (favorite song), this time (oh my god!), wound, the eye of the mourning, the age of innocence, the imploding voice
machina II = intended to be a freebie given away with machina I, another highly underrated collection. the lo-fi nature of the recordings makes it difficult to listen to, but given a chance, the songwriting is striking. some of their heaviest tunes to date, some of their poppiest tunes, some of their lovliest tunes - cash car star, glass' theme, if there is a god, innosence, real love
alternatively, you could start with the greatest hits - i would say listen chronologically, to get a sense of their considerable progression. also, the tune 'untitled', is one of their best. also includes 'drown' - another smashing pumpkins classic.
pisces iscariot collects many b-sides and unreleased tracks from the sessions of the first 2 albums. not a good place to start, but if you're digging/itching for more, there are still more gems to be found - hello kitty kat, frail and bedazzled, whir, starla
i'm personally thrilled they're getting back together. it misses on the nostalgia aspect if it isn't the originals (for the record, i'd take melissa auf der maur over d'arcy any day of the week and twice on sunday), but to have billy and jimmy together making new music and playing the old songs seems well worth the price of admission in my mind. most bands undergo some sort of lineup change, we're spoiled by U2 and radiohead...
ps - that clip sounds like cheap trick! cool...