I want them to lay 250 eggs a year. (very major issue)
Most dual purpose breeds will lay at that rate or better when they are laying well. The problem is that they don't lay equally well throughout the year. When they molt, which is usually in the fall when days get shorter, they practically stop laying. Molt can last from a couple of months to maybe four or five months. Some chickens are fast molters and some are slow molters. From what I know, how fast they molt is an individual chicken thing, not a breed thing. Commercial egg laying operations control when they molt by providing artificial light, but if a hen goes too long without molting, egg production can drop off.
There is another problem. Many chickens drop off in production when in extreme temperatures. Down in The Parish you don't have to worry too much about extreme cold, but you will probably find that production drops in your hot summers. For egg laying purposes in your climate, you are probably looking at the Mediterranean breeds, like leghorns.
They should set every egg we choose to hatch. (Not really a major issue)
Glad it is not a major issue because it is probably not going to happen. Production breeds have been bred to produce. A broody hen does not lay eggs, so she is eating feed, causing extra problems and labor due to special handling requirements, and not producing eggs. There are breeds that often go broody, but in general they are not going to meet any of your other goals. The breeds that go broody a lot are the ones that are kept around for decoration, not production, like Silkies or Cochin. Even these do not go broody when you want them to. They go broody when they want to, which is not always when you want them to. Some production breeds, like leghorns or Rhode Island Reds, hardly ever go broody. Some of the dual purpose breeds, like the Orpington, Australorp, or Sussex will go broody a fair amount, but nothing like a Silkie or Cochin. You may get lucky and get enough broody hens to have a self-sustaining flock, but you may also be looking at buying an incubator.
It would be nice if the pullets dress-out around 3 1/2 pounds. If I have to, I will raise a different breed for meat.
Most dual purpose breeds will meet that goal. Leghorns will not. Not sure what your goals are, whether you are raising them for your family to eat on or if you have visions of selling some. Maybe you have a pet alligator that is a picky eater. I don't know. If you plan to butcher a bunch at one time and freeze them, then you might want to look at raising the meat birds, but these are certainly not self-sustaining and require intensive feeding. They are not foragers. Besides, do you want a freezer full of chicken during hurricane season? If you plan on butchering a few to eat as you go, then the dual purpose breeds probably meet your needs. By dual purpose breeds, I mean Orpington, Australorp, Delaware, Sussex, any of the Rocks and Wyandottes. There are others. The Rhode Island Red was developed mostly for egg laying and the New Hampshire for meat, but they would meet this goal. Buckeyes and Chanteclers were developed for cold weather, not hot, but are possibilities. Then the sex links should be considered. These are not a breed but a cross between different breeds that you can tell male from female at hatch by color or pattern.
The birds should be great foragers that are more than willing to get penned-up at night. They absolutely must use the nest-boxes I provide for laying. My wheels are failing me and, I cannot go traipsing all over the place looking for nests in the weeds.
Penning them up at night should not be a problem for any of them, mainly a matter of training. I've had problems with younger birds getting picked on by older birds that want to roost out of the coop where they don't get picked on, but breed does not matter about that.
I find that my broody raised chickens are better foragers than my brooder raised chickens. Mama does a better job of teaching them than they learn on their own. With that said, if you don't provide them food, the ones that learn that they have to find their own food will provide you a flock that has learned to forage on their own. The others, well, they won't reproduce. I think it is mostly a matter of training. Once the flock learns to find its own food, they teach the newcomers, even if they are brooder raised. I have not done it, but I remember Dad getting a dozen chicks from the Co-op, raising them until they could manage by themselves (around 5 weeks old), and just turning them loose with the flock. The older chickens bully them and would not let them hang around real close, but those chicks learned to forage for themselves. We hardly ever lost any of those. Now, if they forage for all their food, their production may drop some and the young ones may not grow as fast.
Nest boxes are another problem. Most will use the nest boxes in the coop where they sleep, but you will almost certainly find that some look for other places to lay. When I find one not laying on the coop, I lock the flock up in the coop and run for a few days to try to break that hen of that bad habit. It really helps to find her old nest and remove the eggs. That is not always easy. They are pretty good about hiding nests and sneaking on them. I find that if I pen up the flock, the hen that is laying out of the coop paces the fence when it is time to lay her egg, trying to get out to get to her nest. Kind of imagine a hen pacing and trying to cross her legs at the same time. If you let her out when she is like that, she will probably go to her nest, but they are pretty sneaky.
Because I have 10 grandchildren, any mean bird will be instantly "CULLED"! Pun emphatically intended!
The dual-purpose birds I mentioned may produce roosters that attack kids or they may not. It is individual with the rooster, not a breed thing. Rhode Island Reds have a bit of a bad reputation for this, but even some of them are OK. But yeah, any rooster that attacks any human has committed suicide. Nice of them to volunteer for the pot.
Of course, because so many of these grandchildren are girls, the chickens should be beautiful.
It really is in the eye of the beholder. Get a few different breeds or colors and patterns within a breed. As long as all your chickens don't look alike, your grandkids will pick out favorites. I think it is hard to go wrong with any of these breeds.
Good luck!