You might want to look at a 1-4/6x scope of some type. The huge FOV on the bottom end makes target acquisition lightning fast, with a well fitted rifle it is faster than open sights. The 4x or 6x on the top end makes 200-300 yard shots pretty easy.
I use the 1-4's almost exclusively on my combo gun and drillings for coyote hunting, with some practice I can even shoot birds on the wing with the shotgun barrel and scope. One thing nice about the 1-4's is their straight tubes, they can be mounted close to the bore on the combo guns.
they work well on bolt action too
On my bolt actions I've gone to 1.5-6x4?mm scope as they also have the large FOV for close in work and more X's for longer range stuff. Most modern bolt action rifles have stocks designed for larger objective scopes.