Shafi Trumboo,
These are just my guesses based on very limited knowledge of the google api. You might have better luck finding people well versed in the google api on the google api forum.
Since the Google Maps are in Web Mercator, I would assume any cached (tiled) services would also have to be in Web Mercator (102100/3857).
For displaying dynamic services, the ArcGIS Server could project on the fly and so the actual spatial reference of the data could be anything, but for best performance I would guess data in Web Mercator (102100/3857) would be better.
For querying for data, the ArcGIS Server could project on the fly and so the actual spatial reference of the data could be anything. But since I think the google map api works with geographic coordinates, for optimal performance I would guess data in WGS84 etc would work best. (Depending on how the "ArcGIS Server Link" was implemented).
Again, this is all guesses...