Getting it all done - buying a NEW rifle and NEW scope - for $600 is getting tough. A guy almost has to buy a package set, or has to be satisfied with a pretty low-end scope.
The bottom end for bolt rifles tends to be camping around $375-400, which only leaves you about $185 for the optic when you account for taxes, which really puts you in a pretty poor class of optics. They'll kill deer, but they'll often leave you hanging. Bushnell Banner is really the only scope in this class which draws my attention.
Add $100 to your total budget and you'll be able to step up considerably in scope quality. In the $250-300 ballpark, I am a fan of Bushnell Elite 3500's.
Personally, out of your three, now two options, I would buy the Savage, fix the stock or change to a laminate, and drop a Bushnell Elite on top.