This is just my own take on it, but I love Barred Rocks; Barred Rocks or Rocks of any color for the consistency of laying and non-broodiness (generally). They are friendly, curious and lay very large eggs. I have some 4 year olds who still lay several a week.
Buff Orpingtons for the huge eggs, but on occasion, most of them will go broody, especially if they are breeder types over hatchery stock, so you can raise chicks.
True Ameraucanas for sweet personality, blue eggs and just some real variety over single combed breeds. Some do brood.
Delawares for their energy, intelligence, ability to forage very well, friendly personalities and their consistent egg laying ability. Their eggs are very rounded and a peachy tan or pinkish color, very different from the usual brown egg, I find. I love mine, though I generally don't care for white birds. A well-bred Delaware rooster is a big bird and good meat, if you get good lines so they will grow large as they should be. Breeder lines will brood, usually.
There are so many wonderful breeds, though, and it takes trial and error to find out what you really love. There's a chicken breed for everyone!