Green is what introduced me to REM, and it has been my favorite album of theirs ever since.
Yes, all of those, in that order, plus Automatic for the People, Green, and Dead Letter Office (mainly for the Chronic Town songs and the Velvet Underground covers).
But Murmur is the first stop.
Monster is also very good.
Word to the wise: Don’t take musical advice from anyone holding this opinion. 
That’s what I love about opinions. We all have them. Typhoon just doesn’t know the frequency.
;j
Green.
Document.
Monster is very underrated, in my opinion – not that any of our opinions matter, though, since SanibelMan already has it.
I’ll go against the grain and recommend Reveal – I think it’s their best “soft” album since Automatic for the People.
Me, I like DLO for the drunken version of ‘King of the Road’. But then I’m weird that way.
Actually, I have all the albums and can’t pick just one. Get 'em all, in order, from Murmur on.
[sub]What hasn’t been mentioned in this thread yet? Up. Get that one too.[/sub]
I have to put in yet another vote for Murmur, which holds up quite nicely after all these years. After that, I’d say Lifes Rich Pageant, then maybe Fables or Document, and then the others.
Don’t forget, they have a new “Best Of” coming out this month. It’s titled In Time and will have two new songs, “Bad Day” and “Animal,” both of which I think are worth the price of admission.
Strangely enough, Bad Day was written in 1986.
So, it’s old/new.
If you’ve heard the original version of “Bad Day,” you know it’s been reworked to the point that it’s not quite the same song. So it’s new/old. 
Reckoning is my favorite after AFTP. After you’ve bought it, get Murmur. My opinion matters much more than everyone else in this thread.
Up SUCKS.
I found ‘Reveal’ to be quite good too.
But it does have “At my most beautiful” on it which must count for something.
I’ve got an early demo of Bad Day (back when it was called PSA (Bad Day)), and though the quality is really terrible, I like it much better than the new one. It had a lot more harmonica, and the chorus had a bit more of an anthemic quality to it.
It sounds a lot like they decided they’d never release it and so used the chorus melody for ITEOTWAWKIAIFF.
DLO is wonderful for the cover of “Toys in the Attic.”
Well, I bought Document from the iTunes Music Store. So I guess Fang and Angel of the Lord win. I like it, especially “Exhuming McCarthy.”
But if you feel I’ve made this purchasing decision in error, feel free to send me ten bucks and I’ll download the album of your choice. 
I agree with the “Anything before 1987” comment but would have to amend it to “Everything before 1987”
Specifically: Document is one of my favourite albums of all time. But the rest are almost as good. Especially Out of Time. And Green. And Life’s Rich Pageant. And Murmer …
If you did buy everything before 1987, you would be tempted to say that you wouldn’t also need Eponymous, but you’d be wrong, because you wouldn’t have the funky remix of “Finest Worksong” with the horns.
I never considered myself an REM fan until I woke up one day and found I had almost all of their albums (up to and including AFTP, they got bad after that). And this thread confirms my suspicions: you cannot own just one REM album. You have to get them all. While not the best band ever, I would not argue if someone called them the consistently best band ever.
the best band, that is, that Neil Young wasn’t in.