There have been several phases to the Kinks’ kareer:
The Early Years: characterized by simple, hard-rocking singles like “You Really Got Me” and “All Day and All of the Night” and more ballad-y stuff like “Tired of Waiting” and “Set Me Free.” The albums from this period are, like the Beatles’ early albums (though not as polished), a mishmash of hits, covers, and filler. Unless you’re a hard-core fan, a hits collection that includes several of these songs is all you need here.
The Kinks’ greatest contribution to music was in the string of 5 brilliant albums: Face to Face, Something Else, Village Green, Arthur, and Lola (note: some album titles have been abbreviated). All of these are indispensible. Face to Face is, as Biffy said, their first klassik album, and maybe their most underrated; it’s as good a place to go as any from Village Green. Something Else is more uneven and you may already have its best songs (Waterloo Sunset, David Watts, and Death of a Clown), but there’s other good stuff there. Village Green is on the short list of albums I have absolutely fallen in love with. Arthur may be their masterpiece, but it’s more complex than the pastoral simplicity of Village Green, and takes longer to appreciate. Lola is a concept album about the music biz, and its a great one, despite the horrible-looking cover.
Then come the RCA years, starting with Muswell Hillbillies which some people love, but I find it a bit too low-key to be one of my personal favorites. Several of the albums the Kinks made during this period in the early to mid 70’s (Preservation Act 1, Preservation Act 2, Soap Opera, Schoolboys in Disgrace) are sort of like mini-musicals or rock operas or soundtracks to their stage shows of the time—attempts to tell a story and present songs from the viewpoints of different characters. They’re not always 100% sucessful, but they’re fun to listen to if you don’t take them too seriously, especially Schoolboys, which is a fun album if not a great one, and which shows signs of the Kinks actually turning back into a rock band. There’s a best-of from this period called Celluloid Heroes.
Then come the Arista years, from the mid-70’s Sleepwalker through to the mid-80’s Word of Mouth, and including Misfits, Low Budget, Give the People What They Want, and my own personal starting point, State of Confusion (which has their big hit “Come Dancing”). This is their “arena rock”-y phase. Come Dancing With The Kinks collects the hits from this period.
Then they put out a handful of uneven but interesting albums on MCA: Think Visual, UK Jive, and The Road, yet another live album and one that I like very much.
Finally, there was the long, not-bad-but-not-great Phobia and the great-if-you-could-find-it EP Did Ya, and then To the Bone which consists mostly of rerecordings (acoustic and/or live) of older Kinks songs.
There have also been several compilations released, some of which include songs not available elsewhere (the Kinks Kronikles that Crandolph mentioned is one of these, with many songs from roughly the same period as Village Green).
I never met a Kinks album I didn’t like.
(I’ll see what B&N have, since I’ve got a gift card with them)