I actually used to think R.E.M were quite boring and bland and in a group of rock bands there was no edge to their sound, it was just kinda calm and boring. But my dad was a fan so I've been exposed to their music a bit and it's an interesting case of how your outlook on things can change as you grow older. I recently said "screw it" and acquired all their studio albums and my plan is to go through them one by one because I really like the hits and I want to get more into detail.
This is the way to do it. I'm actually a HUGE REM fan, and for me, with only a few exceptions, the more popular a song of theirs is the less I like it (Losing My Religion is an exception, as is Radio Free Europe). Theirs is a catalogue that is best understood as a catalogue. They're a lot like Rush in that regard; there are patterns to their records, there are leaps and starts in their catalogue, there are albums that have songs that are throwbacks, and songs that are looks ahead...
I love the "Out Of Time" album, but the key songs are the ones that didn't really get airplay: "Near Wild Heaven" (which was a single), and what's called the "Memory Side" (side B of the record, for you fogies), with "Belong", "Half a World Away", "Texarkana", "Country Feedback" and "Me in Honey".
A lot of their records - Monster is the best example - are of a kind, meaning they are musically themed. Not that they aren't varied, but you're not going to get a Queen album, which veers from a 50's rocker to a 20's pastiche, to a 70's prog opus, to a dance hall ditty, etc. etc.