I would recommend the first few Ringworld books. (Ringworld, Engineer, Throne, Children) then read the XXX of Worlds. (Fleet of Worlds, Juggler of Worlds, Destroyer of Worlds, Betrayer of Worlds).
You will enjoy the XXX of Worlds more, if you have read more of Niven's Known Space series. The second one, Juggler of Worlds is actually a TON more fun, if you have read many of the underlying stories. Very much like Ender's Shadow, it replays well known stories from the original stories, but from a different perspective. Which like Ender's Shadow is very entertaining.
If not, it looks like a strange set of unrelated stories, trying to be connected, and pretty tenuously.
For example, Carlos Wu's autodoc is mentioned in later Ringworld stories (I think in Ringworlds Children) and we know a little about Carlos, but we see a lot more about him in Juggler of Worlds.