About any chicken can handle very hot, occasional freezes, and rain. The key is a well ventilated coop and shade, as you probably know. I have not had chickens with feathers on their legs, so I don't have actual experience with them and mud. Hopefully someone who has experience will chime in.
Certain breeds do have tendencies, but friendly depends a whole lot on how much you fool with them, especially when they are young. There is nothing unethical about bribing them with food either.
Any of the dual purpose breeds should do well for you. Black Australorp and Delaware top my list for personality, but honestly the Orpington, Sussex, any of the Rocks or Wyandottes, New Hampshires, Turkens, Easter Eggers, or Rhode Island Reds will all work well. For pure egg laying, it is hard to beat Leghorns. They are supposed to be a little flighty but with proper bribery and handling you should be able to overcome that.
If you don't want roosters, the sex links are great possibilities. If you are getting chicks, you take a chance of getting some roosters unless you get sex links. Some hatcheries provide the commercial breeds of sex links, Cackle and McMurray I believe, while others like Ideal cross two regular breeds to make their sex links. I think Meyer gives you a choice. The commercial breeds tend to lay more and larger eggs than the crosses, and may have a few more potential medical problems, especially if you feed them a diet high in protein, but either would probably fit you circumstances well. It is really hard to pick one that won't suit you.
I'd tend to stay away from the decorative breeds, like Silkies and Polish. They usually don't lay that well to start with and they tend to go broody pretty often, which further cuts into your egg laying.
I probably have not helped you any, but I really think it is hard to go wrong.