I guess I've been an amateur linguist since a college course in linguistics, and some training in "strategic languages" thanks to the Cold War DoD. I think I first heard of Greenberg (like you) through his universals theory, and then I read about his work in African and American languages classification through his pupil Ruhlen. (His African classification is now generally accepted, although it sounds like they're still fighting over his 1987 (?) work on Amerind language classification in linguistics departments). Since I'm particularly interested (though not particularly knowledgeable!) about Indo-European linguistics, I was intrigued by the "Nostratic" theory (which as you know has been floating around for almost a hundred years ago, but was not taken seriously until about 40 years ago in of-all-places the former Soviet Union), I was happy to bust my wallet to get Prof. Greenberg's two volumes on his own Eurasiatic theory. I recommend them to you.
I bought vol I, put in an advance order when II came out. It's very sad he died then.
Another interesting book is Sprung from Some Common Source: Investigations into the Prehistory of Languages