From what I've read Dorkings very often go broody, so the odds of you getting a few broody hens in an order are probably pretty darn good. Some of our RIRs are also very broody, they won't leave the nest boxes unless they're empty. We're going to rock the Jersey Giants anyway since we'll be able to free range them long enough to get a good weight off them, but we're also going to get some Dorkings so we have some broody birds.
Even the Cornish X you order from hatcheries will be better than what you buy in the store. You can free range them, they aren't the most eager foragers, but you can encourage them to get some exercise and forage. There are others here who do Cornish X with great success and don't have the leg problems and such that others do, but it's all in how much you feed vs how much they are forced to forage. Anything raised at home will be better than the commercial chickens. Somebody else here mentioned they prefer Australorps as a dual purpose breed because overall--temperament, laying, meat, health, etc--they feel that Australorps just come out on top. We have a couple we might try.
Two of our RIRs are very broody. One of them will only leave the nest boxes when they're empty, and she'll come back as soon as she sees eggs. We're probably going to keep her for hatching our other layers just in case we don't get any that go broody.
I guess many breeds have had the broodiness bred out of them. I mean it makes sense from a commercial standpoint, and with incubators you don't really need broody hens anyway and it might be less hassle in the long run, plus broody hens tend to peck and make a huge fuss when you try to collect eggs. The broody RIR pecks us, and so does one of our Australorps when she's going through her daily 2 hours of "look how broody I am" (she's such a poser).
So part of selecting our breeds includes a decent chance of broody hens, with the exception of the Jersey Giant. We want to be sure we have a few hens around every year who can hatch eggs for us since we want to do it the old fashioned way.

You could pick whatever meat breed you like, and then order a few hens from a particularly broody breed.