Have you considered Buckeyes? They sound like a better choice for your situation than any of the 3 you selected. They seem to be extremely hardy, make reasonably good table birds in a reasonable length of time, lay fairly well, and they're really pretty, and very people friendly. This is accoring to info I've gathered from people who have them, and from websites about the breed, (all of which seem to have copied and pasted identical info) I haven't got any yet myself, but I want to try them soon.
Delawares might be a good choice, too. Same reasons as the Buckeyes.
I can't say for sure whether I've ever had NH's, I've had some red hens with black tails that I don't know what they were. They were heavier than RIR's. Had a pair of them for several years. Never got broody once. Good layers, though, nice big brown eggs. Ate some of their offspring, the roos. Can't say they were very meaty, but they were cross breeds, too. I had an unidentifiable mix breed roo about that time, he was great with the hens, but the offspring weren't very meaty. A fox got him, and we were sad, because he had such a good personality.
I have Brahmas. They have a nice disposition, I've really fond of them, they're lovely. Decent layers, but they're slow to start. SLOW growers. Do you want to wait a year for a large, tough, bird? Good moms. Can be extreme brooders. But over all, not really practical in a situation like you describe. I'm phasing mine out, but I have an unreasonable attachment to my Buff Brahma roo, papa.
I still have 1 BO hen, I've had a couple dozen over the years. Only had a couple of them ever go broody. Had a couple of really mean BO roos. Ate one, gave the other to a drunken neighbor who thought it was funny to have an attack rooster chase his drinking buddies. We've eaten several BO roos that were extras. They're not bad, but not great either. There are dual purpose birds that are better.
It's hard to predict temperament, I don't know if there really are any that you can count on to never become human-aggressive. Likewise broodiness, I read all the time what good moms BO's are. That hasn't been my experience at all.
I don't know if Delawares or Buckeyes will brood. But, you could always keep a few dark Cornish hens, they brood like mad. Very good moms. Some of the best I've ever seen, in fact. Very hardy, too. They lay smallish eggs that you could mostly tell from the others, at least once they get past the tiny pullet egg stages. That way you could chose eggs from the Bucks or Delawares to hatch. I'd like to try Cornish roo over Buckeye and Delaware hens, too, as well as Dorking, to see what that cross will produce.
You might consider getting an incubator, if you end up with hens that won't brood. You'd get better egg production, and you could control when you have chicks to raise. Maybe keep a standing flock of 15 or so for eggs, and incubate 15 or so at a time to raise for meat.
If all you have are tough, older birds, they still make great meals. The crock-pot is my friend. I got mine for about $4 at a Peddler's Mall. (a chain of flea markets in my neck of the woods) With a removable crock. I love it, but I use a heavier glass lid, not the little thin one that comes with it. My heavy lid holds the heat better.
Now after all that, Floridachickenman's right, you'll have to figure out what works the best for you. I just don't think the 3 breeds you're set on would be the best choices, but if they end up being what
you prefer, that's all that matters.
Good luck in whatever you choose, I hope you'll post how it works out for you.
