From the looks of things, there are a few folks on this thread who are probably around my age, talking about seeing concerts in the 80's, and then there are some who are, well, a lot younger....
I've been in the position before of posting with younger people saying things like, "wow, I've discovered Pink Floyd, where do I start???"
I generally NEVER recommend having people start with collections or greatest hits albums. Yes, you get the radio tunes. But I think you lose a lot by doing it that way. I think it's very easy to become complacent once you have the greatest hits, with a distorted misconception of "I already have the good stuff, so I'll just stop here." You also aren't really able to get the feel for where the band was at a particular point in time by just listening to a collection. I feel that the only way to do it is with the actual albums.
When someone says "Which Pink Floyd album should I start with?" I would never recommend something like "A Collection of Great Dance Songs," I send them straight to DSOTM. Without getting into a discussion of which is the best Floyd album, that one tends to hook people and leave them dying to hear more. I think Moving Pictures and 2112 have the same effect for people who appreciate the sound of Rush.
So I have to disagree strongly with the Chronicles and Spirit Of Radio Greatest Hits recommendations, although if you're just looking for a greatest hits album, those are the ones.
Also, I had Exit Stage Left on vinyl, and while the performances are great, I was never a huge fan of the sound quality, I think the Different Stages collection sounds FAR better. I'm also never a fan of a live album that has fade ins/outs and pauses between the tracks like ESL does. And the disc 3 of Different Stages, which I believe is either from the Fly By Night or Caress of Steel tour is a real treat - it gives people a feel for what they sounded like when they were much more of a heavy metal band, with a screeching Geddy Lee, along with a 2-cd collection with a lot from the second half of their catalog. For a live collection, I stick with the Different Stages over ESL. Oh, yeah, it also has 2112 start to finish - even All The World's A Stage is missing pieces of 2112
So my original post was 5 albums that you can't go wrong with. But in reality, what I would say to do is to start with 2112 and Moving Pictures. Then you're hooked. Then start from the beginning with Rush, Fly By Night, Caress of Steel, and move on from there. By doing them in order like that you can trace the fascinating musical transitions that this band has gone through.
Also have a watch of the R30 dvd, it is superb.
And keep those fingers crossed for another tour!!!