BCowan,
I don't know where you are located so I'm not going to get into what grass is best for your specific site, but I have a hard time thinking of any location where Rye grass would be my first choice.
It does establish quickly, and it is dark green and stripes beautifully, if you are in to that.
But, over the long term, it is not as durable, drought tolerant, disease tolerant, and IMO nor does it provide as good a golfing surface as you can get with other turfs.
Used as an overseed it does very well as demonstrated by that little golf tournament in Augusta every spring. But take away the Bermuda base and play on it year round and I don't think you'd be happy.