Even a .223 will knock a target down at 300 yards. Trust me. I've done it. Thousands of times.
I've knocked down targets at 300 yards (meters) with a 5.56, too. A lot.
AR, it's got a 16 1/4" barrel. It's the carbine version, but I like it a lot. Thing is, I promised my wife that I'd get her an 870 Synthetic in 20 gauge. A couple of my friends told me, "She'll just shoot you in the back with it." I told her that, and she smiled and said, "I'd never shoot you in the back." All I ask is to see the damn shot load coming.
I've also got my eye on a Marlin 1894C in .357 Magnum, too. If you want to see why, go to the thread on the .357 Magnum in the "Living Off The Grid and Survival" forum.