There are basically two kinds of chicken you can buy: crossbreeds—also known as hybrids, and breeds.
Crossbreeds — commercial colour-sexed browns
Crossbreeding—also called hybridization, is a common strategy for maximizing yields in agriculture, with the crossbred plant/animal being superior in performance to either parent. As the term implies, crossbreeds are produced by the mating of two or more different breeds together. Hybrid colour-sexed browns (CSBs) are the mainstay of the Australian layer industry and include the Hy-Line Brown (Hy-Line International, Erich Wesjohann Group)—probably the most common , Lohmann Brown (Lohmann Tierzucht, Erich Wesjohann Group), ISA Brown (Hendrix Genetics) and Bond Brown (Bond Enterprises, Queensland). CSBs lay a brown egg (light-medium), which is the Australian preference. Their production involves a convenient colour sexing strategy : when a gold cock is crossed with a silver hen, female chicks have brown down while males have yellow down. For example, among common breeds this is seen when a Rhode Island Red cock is crossed with a Light Sussex hen . This cross produces a CSB known as the Blacktail, popular in the United Kingdom. Both breeds have the columbian gene, which gives the black tail and neck feathers. While Hy-Lines, Lohmanns, ISAs etc. were developed separately, they look alike because the feather colour genetics for sexing is the same and they have been selected for similar performance traits. With this in mind note that the name ‘ISA Brown’ is often used generically for any CSB.
The gold and silver breeds crossed to produce the commercial CSBs probably do not correspond closely to any known breed, although youll come across anecdotes to the contrary. For example, it is sometimes claimed that the ISA Brown is a two-way (two-breed) cross between a Rhode Island Red cock and a Rhode Island White hen, although there is no evidence for this. On the other hand it is probable Hy-Line Browns derive predominantly from Leghorn varieties . Regardless of the orginating breeds, after decades of selective breeding to improve performance of the hybrids [5,6] the commercial breeds would now be distinct, with their genetic profile known only to the company. Lohmann Browns are produced from a four-way cross  and indeed virtually all commercial poultry worldwide are produced in this way . An exception is the Bond Brown, which is a two-way cross between a Rhode Island Red cock and a Rhode Island White hen—as stated on the company web site.
Non-colour-sexed hybrids you can find are the White Cross (New Hampshire Red × White Leghorn), Red Cross (New Hampshire Red × Rhode Island Red) and Black Cross (Australorp × New Hampshire Red) . In these two-way crosses between known breeds, if the breeds used have not been closely monitored and selected for laying performance, it is likely the performance of the hybrids will be variable, i.e. variability in the breeds used as parents will be passed in some measure to the hybrids.
There are numerous breeds of chicken—also called purebreeds, pure lines, inbred lines, lines, strains, etc. because they breed true. These have been bred for eggs, meat, looks, or a combination thereof [9-12]. The Leghorn was the most important layer in Australia and remains as such in the USA. It lays a white egg, the American preference—along with white bread. Personally I like the look and personality of the Barred Plymouth Rock (an American breed), Buff Orpington and Light Sussex (two English breeds). However these large dual purpose birds—for eggs and meat—eat a lot of food, do a lot of poop, and often go broody. The popular Australian Langshan lays well, is not particularly broody, is medium-size with a good food-to-egg conversion ratio, and is reputedly a good winter layer (lays well without the need for add-on light). The consensus is that the best laying breeds are the Australorp, Leghorn and Rhode Island Red.
It’s less hassle to buy chickens near or at point-of-lay (~20 weeks), so you don’t have to keep them long before they start laying. Buying them as hatchlings means they must be kept warm with a brooder until they develop feathers, and it’s a long wait before they lay—at least six months. Of course, your kids may really want those cute fluffy hatchlings. If you want a particular breed, you may have no choice but to buy hatchlings or young pullets.
If you primarily want eggs and don’t care much about anything else, then hybrids are the clear choice. The ubiquitous CSBs are bred to lay—with good consistency from hen to hen—and are unsurpassed in performance. Also they can be sourced at any time of the year, and probably are already vaccinated if purchased from a larger commercial egg farm. Someone might tell you they get cancer or don’t live long. This is hearsay and essentially irrelevant because if you just want eggs it’s best to replace them after two seasons—still early in their potential lifespan. If you find them unattractive then the White/Red/Black Crosses can provide some variety. These can lay as well as the CSBs, although my own experience has been high variability in performance from hen to hen—i.e., you are likely to get some duds. Whatever you get it’s about finding the right balance between your own taste and requirements.
1. SBA celebrates 25th anniversary of Hy-Line Brown in Australia, Poultry Digest, Oct/Nov 34(2): 30 (2018)
2. Gender identification of chicks, Hy-Line Management Guide
3. Gold and silver sex-linkage, Daniels T. (2010) poultrykeeper.com
4. The ‘scientizing’ of breeding in the North American egg industry, in Art and Science in Breeding: Creating Better Chickens, ME Derry, University of Toronto Press (2012), ISBN 978-1-4426-4395-6
5. Tixier-Boichard M, et al. (2012), A century of poultry genetics, World’s Poultry Science Journal, 68: 307-321
6. Breeding, Lohmann Tierzucht
7. Lohmann Parent Stock Guide , Lohmann Tierzucht
8. Cross bred chooks, Burke’s Backyard
9. Chicken Breeds in Australia, Poultry CRC
10. Chicken breeds, poultrykeeper.com
11. Chickens, Poultry Club of Great Britain
12. Chickens, Omlet