Free floating a barrel often improves accuracy. Won't have much effect on cartridge selection.
As far as a good cartridge for deer hunting, it depends as much on you as anything. Are you a good hunter? A good shot? Can you handle heavy recoil? Will you hunt close heavy cover or open fields?
In my opinion a cartridge that can shoot at least a 115 gr bullet to at least 2800 fps second is a good place to start.
Heavier bullets or higher velocity makes longer shots easier.
Leo
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