The best egg layers do not go broody.
A broody hen does not lay eggs while she is hatching eggs and raising chicks.
You might want to have more than one breed: one that is good for laying eggs, and a few hens of another breed that is good at hatching eggs.
A broody hen does not care if she sits on eggs she laid, or eggs laid by another hen.
Most kinds of bantams are good broodies, so you could keep a few bantam hens to hatch the eggs from your other hens. Because the bantam eggs are smaller, it would be easy to tell which hen laid which eggs. And the small hen can do just fine with large eggs.
I've had a few Old English Game bantams that would lay 12-20 eggs, go broody, raise chicks, lay another 12-20 eggs, go broody again... So they spent more time broody than laying, but were convenient for raising one batch of chicks after another all summer long. Many people like Silkies for broodies, but I prefer normal feathers, clean legs, and no extra feathers on the head or face. So the Old English Game Bantams were a good choice for me.