Hello

and Welcome To BYC!
The best place to find local birds is usually to post on your state thread
https://www.backyardchickens.com/t/121387/yo-georgians this time of year most feed stores like
TSC also carry chicks. Also try the BYC Buy-Sell-Trade forum.
Here are a couple of charts that compare different breeds
http://www.sagehenfarmlodi.com/chooks/chooks.html and
http://www.albc-usa.org/documents/chickenbreedcomparison.pdf and don't forget to check out the BYC Breeds section for member reviews for a lot of breeds when you've narrowed down your choices.
For pets,especially for children, Silkies and Cochins are probably the two most popular breeds, they are not very good egg layers but are very friendly... Silkies do have special needs, and often have to be kept separate from other breeds, so take that into account if you decide to get some. So far as more layer breeds go, for egg numbers alone, the Red Sex Links (Golden Comet, Red Stars, ISA Browns etc) for brown eggs are probably the most popular layers around. 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 breeds that are usually pretty easy to get along with, they all lay different shades of brown eggs. The Easter Egger, often sold as Ameraucana by hatcheries, are a fun breed because they usually lay green/blue eggs, and they tend to be very nice birds, and then there are the Welsummer and Marans for dark brown eggs. You might also like to check out your state thread to see what people in your area have that they are happy with.
One note, when you get birds of different ages you do have to be careful combining them and wait until the younger ones about the same size and do it gradually, here is a nice Learning Center article on adding to a flock
https://www.backyardchickens.com/a/adding-to-your-flock