Something like the frying pan special, all large breed rooster chicks is pretty cheap per chick. But I think you will find that the cheapest meat will be from good Cornish Cross chicks, raised with good food, and slaughtered at the right age. The chicks cost more, but the feed cost to raise them to butchering size will be much less.
Actually, the cheapest chicken meat is the bagged fryers at the super market, especially if you get them on sale. I've seen them for as low as 70 cents a pound. You can't raise chicken for that.
If you are uncertain about raising meat birds, if you can wait until spring, most feed stores sell Cornish Cross chicks and you can buy a small number. Say 5 to start with to make sure you like the project.