Hi Maryannkent and welcome to BYC! If you want a brown egg layer you are going to want birds that come from the APA (American Poultry Association) American and or English class. These include birds such as Rhode Island reds and Whites, Plymouth Rocks, Sussex, Orpingtons, Australorps, Wyandottes, Delaware's, and New Hampshires are some of the common ones I find in feed stores commonly. But those are only the purebreds, they cross certain birds together to get birds that lay more often such as sex-links and others. Most birds lay according to their color of earlobe such as red. White earlobed birds tend to lay white eggs. There is no nutritional difference between brown and white eggs since all eggs start out white and get pigmentation later in the laying process.
Good luck on finding your birds, where do you plan on purchasing chicks?
Hello and Welcome To BYC! X3 for egg numbers alone, the Red Sex Links (Golden Comet, Red Stars, ISA Browns etc) and Black Sex Links (Black Stars) for brown eggs are probably the most popular layers around. Production Reds or hatchery Rhode Island Reds are another good choice for layers. If you want breeds that don't lay quite as well but will lay for a longer time, Australorps, Orpingtons (lots of people really like these, great pets though broody), Plymouth Rocks, Sussex, Delaware and Wyandottes are some other popular brown egg breeds that are usually pretty easy to get along with.