Lots of good cartridges listed here. Anything from a 243 on the low end to a 300 mag on the top end. 200 yards is not that far. What's more important is what you are most comfortable with and what you shoot the best. Or I should say what you are most accurate with. For example, a 7mm mag will shoot a 140gr bullet fast and flat. But if you don't tolerate recoil well that might not be the best choice for you. Maybe a 25 06 or a 6.5 creed would work better. Deer are not hard to kill. just use a good bullet and put it in the right place. Personally I deer hunt with a 260, 6.5 Creedmoor, 270, 7mm 08, 280 AI, 300WSM. All very good calibers easily capable at 200+ yards. If I had to pick just one I guess it would probably be the 270.