I have a Savage Model 24, 223/12 gauge. I love it for brush, or hardwoods hunting. The 223 is accurate to about 150 yards, and the 12 gauge is good 40 to 50 yards with the modified choke. I use a red dot scope which works well for both barrels. I set the red dot up at 100 yds. for the rifle, and just look through the scope without the dot for the shotgun, and it is dead on. A regular scope would be a problem just as beagler said he had expeienced. I originally thought about a regular scope with see through rings, but went with the red dot instead.
I chose the 223 because the ammo is cheap, and you can find it anywhere. If I had it to do over I think I would get the 22 Hornet/12 Gauge.
I think the Hornet combo is what I need too. Most of my shots are less than 100 yds., and the 223 does a lot of hide damage on the thin skinned critters like fox, and bobcat at that range. The 223 shoots 1/2" groups at 100 yds. I have an older Savage Model clip fed 340E in 22 Hornet with a Weaver 2.5 X 7.5 that I traded for at a gun show last fall that I really love to shoot (it shoots 1/4" groups at 100 yds,), but I don't like having to carry it, and a shotgun both at the same time. I didn't buy the Hornet until after I had already bought the 223/12, so I didn't realize how much better the Hornet was for my calling situations until after I had already bought the 223/12. I special ordered the 223/12, and when I did they had it, and the 22Hornet/12 for the same price. I already had several 223's, an AR15, Handi Rifle SB2, and a Pre ban Mini 14, so I had a lot of experience, and surplus ammo with that caliber. Thats why I purchased the 223/12. You know the saying "Hind sight is 20/20.