White leghorns or the hybrid cross birds are the best of the best but I consider them to be uninteresting and they can be very difficult backyard birds. They also often die at a very young age from just laying themselves to death. I prefer older heritage breeds which live longer and are more interesting to me. I also like colorful eggs.
I agree with Henry. Speaking from the perspective of someone who has lost 6 hens to internal laying in the last year or so, I want them to take breaks for molting, going broody on occasion, etc. They'll live longer. The super high production layers are much more prone to that ailment. The ones I lost were all hatchery stock and included Wyandottes and Rhode Island Reds.
For brown egg layers that will lay like hell for two years I would go for RIR, BR, Black star, Or red star. These are the birds that speckledhen is talking about bred for laying and will give out after two or three years but they are the best layers.
Depends on the lines they come from. Most hatchery stock is bred to lay continuously, though it's not really natural for some breeds. An Australorp holds the world's record for laying, however, many do not lay nearly that well.
Any production cross. Red sex link, gold sex link, black sex link. Those all lay brown eggs but, like people have already stated, are not good throughout their whole lives. They usually die early and even if they live past two years they won't lay anymore.