I spent a fair amount time shooting benchrest and often shoot as quickly as possible to eliminate (as much as possible) the effects of changing wind. As I use both stainless and CM barrels in target rifles with no discernable effect, I doubt that the type of steel in a sporter rifle barrel would matter much. Overall barrel quality does make a difference but that has many factors other than the basic material.
To the OP: Bedding the action and free floating the barrel are inexpensive improvements that normally makes a 700 shoot better. This is most notable in rifles firing harder recoiling cartridges. An aftermarket trigger is also nice.