What are some types of hens that lay large or many eggs?

Leghorns! They lay an avg. of 300 per yr. They lay very large eggs for their little bodies which require less feed than other "good layer" breeds.

Rhode Island Reds are very popular because of their dual purpose. When eggs production wanes, they can be eaten. They lay an avg. of 200 per yr. Orbington Buffs are comparable to RIR.

Barred Rocks are also Excellent egg laying chickens.

Red Sex Links (also known as Red Stars) lay up to 280 eggs per yr.

There are a couple of others that I am not as familiar with but everything I have read (and experienced) rate Leghorns as the best. These are the white chickens that are used for commercial egg production.

Free range/ organic white eggs are just as nutritious as free range/organic brown eggs. Brown eggs simply have more pigment making them appear "richer".

Commercial white eggs are not as nutritious, hence some of the confusion