Funny you should say that, I spoke with several hunters in Colorado this year that hunted Elk with a .243.
25-06 for the win perfect Oklahoma rifle coyote and deer killer.
While I agree with this a different idea that fits the OPs need may be a levergun in .44 magnum. It would be capable of killing deer at 200 yards and .44 special ammo could be used for plinking.
Maybe even a Ruger bolt gun in .44 or .357.