Hi there Bigdawg.
The Remington 597 wouldn't be my first choice for a .17HMR - but if thats what you like then go for it. In my opinion you would be much better off with a bolt gun - They are more accurate, and more reliable. As I mentioned, the accuracy of a bolt action .17HMR such as a Savage, Marlin, or CZ 99% of the time would most likely out shoot the Remington 597.
If you are just looking at a .17 semi auto there are other choices out there such as the Marlin 717 I believe, or if you can find it; a Ruger 10/22 mag with an aftermarket barrel (Green mountain is very good) will be very accurate and reliable. I am not sure if TC (Thompson center) makes a .17 in semi auto but I do know that their .22 semi auto's are very good. You might want to look into that if they do make a .17.
On my .17HMR I have a Bushnell Banner 6-18x50. So far it has worked real well for me and has been real reliable.
Jordan