Nashville is rotating Ellis and Rinne. Ellis did great 2 seasons ago, but Rinne won over last year. Ellis outperformed Rinne in the pre-season so he's got the slight edge again, but right now they are literally splitting starts.
I think Giguere will win over Hiller, and will play at least 50 games. Hiller wouldn't be a bad 3rd option, but I wouldn't count on him as one of my two top goalies.
Not sure about Varlamov. Theodore has the starting role for now, but he's on a short leash.
Huet will be the clear starter in Chicago, but Niemi will push for playing time.