Love my Model Seven in .308. It's definitely hunting accurate, which is what I use it for. But I don't put lots of rounds down range through it on a regular basis, so can't comment on it as a target gun. But I consider it a great general purpose rifle. That said, since you're NOT planning to hunt with it, I think I'd look at the .243 or the 7mm08, either of which should shoot flatter from the Seven (but both of which would be plenty for whitetail or self defense if needed).
Given your handgun selections, though, I'd also consider a lever-action in .44mag (even though you said you prefer a bolt). 200 yards would stretch it, but it would be great out to 150. A Marlin 1894 with full-length barrel can hold 10 rounds in the magazine. And GeorgiaArms "deer stopper" ammo will give you plenty of recoil. And it make a great plinker with .44 spls. If you want irons, I'd set it up with XS Sight Systems ghost ring set. And in my humble opinion, the straight stocked 1894 looks far prettier than the 336's curved pistol-gripped stock. And if you're planning to use your GP rifle for self defense, the .44s are less likely to overpenetrate than the .243, 7mm08, or .308.
Let us know what you finally decide on.