1. Rhode Island Red.
These guys are the jack of all trades. Originating from New England, they are very cold hardy, but can handle heat as well. They are great layers of large brown eggs, and very meaty birds for the table. Rhode Island Reds are decent free-rangers but will still need some supplemental feed, even in the summer and fall months. Roosters are extremely strong and protective of the flock, but this also means that they tend to be aggressive. Make sure children know to avoid the rooster and what to do if it becomes aggressive toward them. Hens are mildly broody, meaning they will hatch and raise chicks occasionally.
Heritage birds (from a breeder) are desired over hatchery stock for this breed. Hatchery stock Rhode Island Reds (also called "production reds") have been bred for excellent egg-laying, sacrificing broodiness and size, so they are less desirable for dual-purpose uses. However, hatchery stock will still be good enough for the average prepper. Mine come from hatchery chicks! This would be an excellent breed to make up the bulk of your flock.
2. American Game
American Games are the fighting fowl of the US. These beautiful birds are probably the toughest common chicken you can get! They are extremely flighty, and can evade most predators with relative ease. Their wings and tails are very long in comparison to their body size, making them perfectly equipped for flight! What they can't fly away from, they will fight. Because females often grow spurs as the males do, they are a force to be reckoned with to predators. Females are also excellent mothers, going broody and raising chicks several times during the hatching season. They protect these chicks with ferocity.
In addition to being very good at protecting themselves and their young, this breed is very hardy and self-reliant. They can handle both heat and cold very well, can eat almost exclusively through free-ranging. Owners of this breed find that they often prefer to roost in trees rather than in coops, no matter the weather! They are practically wild birds, and can adapt to most any climate. They can have a pea comb or a single comb. Pea is preferred in cold climates, while single may be better in hot climates.
The hardiness of this breed comes at a cost. They are not bred for production, so hens lay less than 100 eggs a year. Though they are muscular, they weigh less than five pounds, not making them much of a meat bird. In addition to that, these birds are born and bred for fighting and are very aggressive. Males can not be kept in confined environments with other males. Because of this, games should not make up a big part of your flock. Due to their flightiness and aggression, games are not ideal for beginners.
3. Plymouth Rock
Stocky and cold-hardy, Plymouth Rocks are my personal favorite dual-purpose bird. They lay almost as well as the Rhode Island Red, but lay slightly smaller eggs and may lay a little less per year, especially comparing hatchery stock. They make up for it in their meat, however. Plymouth rocks are heavy, meaty birds. Both male and female can dress out at a decent size, and make for a tasty roast! Males are fairly protective, and not very aggressive. Females are moderately broody, and their size means that they can hatch a lot of eggs at a time.
While they will free range, their size requires that they have a lot of feed to supplement what they find. This also means that they are poor flyers.
Plymouth Rocks come in a lot of difference colors. Especially for free ranging flocks, barred or partridge colored varieties are best. White is the most easily spotted by predators, but the white pin feathers look better for butchering than that of darker birds.
4. Orpington
Orpingtons, the pillow-pet of chickens. You can thank England for this fluffy breed, where they were developed into the excellent dual-purpose bird that they are today. They do fairly well in free-ranging, but will still require some feed, all seasons. Some people prefer Orpingtons over any other breed as a mother to chicks. They are very large, so a lot of eggs can fit under a hen. This breed also has an extremely calm, friendly temperament, making them a common pick for families with children. Roosters are generally not extremely protective, however. This breed is particularly cold hardy.
These birds have been bred for both eggs and meat, and lay medium to large eggs. Because they are a heavy breed, so each bird will have a hearty amount of meat for butchering. The most common color is buff, but they come in many more solid colors as well as patterns!
5. Leghorn
Sometimes pronounced "leg-horn", sometimes pronounced "leggern," Leghorns lay most of the eggs you see in the grocery store. This is because they are able to produce very large eggs, while their small bodies require significantly less food. In addition to laying lots of eggs on little food, they are great at free-ranging and excellent flyers! The brown variety of leghorn will be less susceptible to predators than the more common white. Males are known to be protective and are prone to aggression. They are generally not a mothering breed, however. They go broody very rarely.
Leghorns will do very well in hot environments, but may do poorly in colder climates. Their large, floppy combs are prone to frostbite in the extreme cold.
6. Easter Egger
The Easter Egger (often abbreviated 'EE') is not a true breed, but rather a mix of a blue laying breed, usually an Ameraucana or Araucana, with a brown or white layer. They generally lay blue or green eggs, but can lay pink, brown or cream as well. Hatcheries often label Easter Eggers as "Americana" to fool people in to thinking they are getting a great deal on the rare and expensive "Ameraucana" when they are, in fact, getting a mixed-breed bird.
Nonetheless, Easter Eggers are inexpensive and extremely hardy birds. They are not very big chickens, but very resilient. They can handle heat or cold, but can deal with extremely cold temperatures better than most. An excellent choice for a northern prepper, EEs are great free-rangers and generally come in camouflaging patterns. They are mildly broody and make good mothers. They are a good layer of medium to large eggs that can be any color, but are most often blue or green.
Easter Eggers are generally known to be quite friendly birds, but it can depend on the breeds a specific hatchery or breeder used in their birds' development.
Breeds to avoid
There are plenty of birds not mention in my list that will do just as well as the above birds in a doomsday situation. However, there are a few you should probably avoid.
Sebright
This breed is often in bantam bins at feed stores. They are striking in appearance which makes them tempting, but your main flock is best without them. They don't lay much, sometimes only laying a total of 4-6 weeks out of the whole year. They don't generally go broody, and they aren't particularly weather-hardy. Males have "hen feathering" due to a mutation that mutes the testosterone receptors in their skin that cause most roosters to have long, pointed, shiny hackle and saddle feathers. This mutation has led to reduced fertility among male Sebrights. They can, however, fly better than most chickens and mine do very well in a free ranging environment (guilty as charged, I have two.)
Silkie
Another I am guilty of owning. Silkies are an Asian breed of chicken that lack 'hooks' on their feathers. This causes the feathers to appear fluffy, as if the chicken has fur. Unfortunately, this mutation causes a lot of problems for the Silkie. They are unable to fly because their wings and tail cannot catch wind. They also cannot handle cool or windy weather very well. Normal chickens stay warm by trapping air between their feathers and their skin. That air is warmed by their body heat, and insulated by their feathers. Silkies' feathers don't do this very well. They also are not water resistant like a normal chicken's feathers, so they get soaked to the skin any time they get wet.
Silkies do have a very calm demeanor, do well in confinement, and are good at raising young. They
may be a good option if you needed to keep a chicken indoors.
Anything "frizzled"
It may be tempting to buy these adorable chickens that look like their feathers are permanently ruffled. However, they run into the same problems as Silkies. Those up-turned feathers are unable to insulate body temperature, making both excessively hot and cold weather difficult for them to handle.
Polish
I personally do love the appearance of these goofy looking birds, but they aren't the best for a prepper. They lay modestly, but generally stop completely in the winter. They rarely, if ever, go broody. Polish could be good free-rangers, if it weren't for their giant crests making them predator bait. The crest blocks out most of their sight, making them unable to see any aerial predators. They also run into problems with other chickens who have not been raised with crested birds. They will peck at the crest, thinking they're getting some funny thing off of their flockmate's head, but they're actually scalping her.
Your own flock
The best flock for a prepper is a varied one. As generations go on, the flock will combine their genes to produce well-rounded and diverse offspring, allowing you to continue your food source for a very long time. The chickens I specified are my personal top picks, but what you like or need may depend on your unique situation. Always do research on a breed before buying to see if it will fit in to your life!