I'm between these calibers: .22 BR, .222 Remington, and .223 Remington for 100 and 200 yard informal bench shooting. I know the .222 has a proven history of accuracy but wonder if the .223 and .22 BR could be just as good with today's reloading tools and components. The rifle I'm getting will be chambered in .22-250 but I have read that it will probably not be quite as accurate as the ones I'm considering. But, that is just what I've read. I don't have enough experience with any of them to make a judgment.

Which would you pick??