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?