Talking about ranges to 200 yards this implies stand hunting to me and I would try the 300BO in a Contender frame with a 14" barrel. If you were stalking or looking for a woods gun, I would go shorter, but you've already got better options for that. If you want a gun that will do both, the 12" barrel will work but you will lose a touch of velocity. If you go with a custom barrel you can pick your length. Check the reloading pages to see if there is any relevant loads.

Shooting 30-30 in a similar setup with similar velocities and bullet weights i would call the recoil quite mild. I would put the recoil between a 38sp. and 357mag in a 6" GP100. In the heavier encore, I would imagine there would be almost no recoil.
For me the platform would be too big and I would definitely go contender, BUT if you wanted to get a bigger boomer in the near future, then maybe getting an encore would be the way to go as a starting point for a family of barrels.