Where are you getting the rooster? If it is from a hatchery it probably doesn't matter. Hatcheries don't breed for meat birds. You are not likely to find much difference in a hatchery Barred Rock and a hatchery New Hampshire. If you can find someone that is breeding either one, a Delaware, or some other dual purpose breed for meat you are probably better off with whatever they have.
Another issue with hatchery cockerels is that they are tremendously inconsistent. I once got 18 Buff Rock cockerels to pick a flock master. There was a tremendously huge difference in maturity and size at the same age. I rejected 15 of them from consideration without even trying, the final three were so much better. If you go with hatchery birds I suggest you get a lot and only keep the best one. Eat the rest.
A New Hampshire will make black sex links with your Barred Rock hens. I don't know if that is a consideration for you.