Confession: I have not yet heard Fear of a Blank Planet. It was a new album when I was first introduced to the band and I was wary of starting there, so I never got around to it. I also haven't heard The Sky Moves Sideways or Signify, so keep that in mind.
I'm kind of inclined to tell you to listen to Signify first out of those three ... I rate it the lowest as a whole, but you should love Waiting Phase One.
That said, if you want something along the lines of In Absentia or Deadwing, FOABP is the place to be, especially Anesthetize, which is amazing.
And The Sky Moves Sideways is how to record a fucking good Pink Floyd covers album without actually covering any of their songs.