Sagan's Contact is worth the read, I think. It owes a lot to classic sci-fi (where human behaviour and bureaucracy more affect the outcome than the "science" does).

One thing is that there is Science Fiction, and then there is Space Fantasy, and the background one should read to know where modern writers are influenced is slightly different. You don't need Asimov to know Larry Niven, but knowing Asimov or Clarke really helps to know where Carl Sagan was coming from.