All the 4Hers I've seen with meat birds raise Cornish Cross (CX). These are the industrial standard meat bird - supermarket chickens - capable of reaching 4-6 pounds in about 8 weeks (as opposed to about 24 weeks for a heritage breed) and boasting a very good feed conversion rate. Some people claim they are prone to health problems and will tell you to expect high death rates due to heart attacks, organ failure, etc. In my opinion, if you're seeing that, you're doing something wrong. I've had batches of them out in 90F degree summer heat and haven't had a single one drop dead inexplicably, ever. However, they are a bit disturbing when you first get them; they have one job - to grow grow grow - and they do it very well. They are extremely messy and walk like obese penguins. The most common health issue seen is a bit of limping (this is the only real problem I've seen in mine). They are also very, very docile and sweet, which sure is a hassle since you have to eat them (these are NOT pets, mind you, and should never be kept past appropriate butchering age, which should be 12 weeks at the latest). This is the most efficient and economical choice and the most popular. Drawbacks include potential health issues, and the fact that they are basically poop machines.
If you would rather have something a bit more "slow food", consider colored broilers. These are large, heavy birds, usually reaching weights of 4-6 pounds in 12-16 weeks. They have a good feed conversion rate but not as good as CX. They lack the double wide breast of the CX, but are still a meaty bird. They are oftentimes Black or Red in plumage. This bird will have a bit more flavor than CX, and displays no more health issues than the average chicken. They are also able to grow to maturity and breed and females are decent layers. Drawbacks include more time/money required to raise, cockerels may begin to have "rooster flavor" starting around 12 weeks, and cockerels may begin to act a bit rowdy in the weeks prior to butchering age.
The last option is a heritage breed. This can basically be any decently meaty bird but in my opinion the only heritage meat bird really worth raising is the Standard Cornish. The Cornish is an ancestor of the modern Cornish Cross (hence the name) and I have found both hatchery and breeder stock make excellent meat fowl. You can expect 4-6 pounds in 25-30 weeks (they are slow growing) and a nice, meaty body. The feed conversion rate is a bit worse than that of the average laying hen's. Cornish with exhibition bloodlines will probably resemble CX quite closely once plucked and gutted. They are good options for anyone wondering what it's like to raise a REAL meat bird and who has plenty of time and space. Keep in mind that roosters will be acting like roosters by the time they are ready for butcher, and will possess gamey "rooster flavor" and be somewhat tough. Hens will be a bit tougher than CX but not tough like roosters. They do not show the health problems associated with CX and in fact are very harsh and sturdy birds.