I loved the Monkees music from the television show. Then I found out that the Monkees weren't a band but just a bunch of actors playing a band on TV. I still liked the music but kinda lost any interest in them as a band.
We're they Milli Vanilli before Milli Vanilli?
Well, not quite, because Milli Vanilli (IIRC) didn't even do their own singing, but lip-synched everything. The Monkees really sang, but they had studio musicians doing most of the instrumentation—but that was only on their first two albums (The Monkees and More of the Monkees); beginning with their third album, Headquarters, they did most of the playing as well as the singing.
Two of the Monkees—Mike Nesmith and Peter Tork—were already accomplished musicians when they got picked for the Monkees. Davy Jones and Micky Dolenz were actor/singers, but they also learned to play instruments after joining the Monkees. The band needed a drummer—because even though they had studio musicians for the albums, the four guys had to play some of the instruments when they did concerts—so Micky learned the drums, as well as some guitar. Davy also learned guitar and bass, and a bit of drums, but his main instrumental contribution was "other percussion"—tambourine, maracas, etc.
All of that to say, if you liked the songs on the show, you'll like much of the rest of their vast catalog—they've done a total of 13 studio albums (9 in the original run, 4 during their reunion years of the mid-'80s to the present), and their label also released, back in the '80s and '90s, three albums of previously unreleased material from their original run, which have some awesome tracks on them.
The Monkees story is actually quite fascinating. The fact that they did not form "organically" makes their success, in my opinion, even more amazing.