Around here it is goats. The price of a goat seems to be pretty solid, between the meat market, people wanting them for 4H and people wanting them as pets and their relative low cost on the feed end it makes sense. The market for a private sale meat goat to the middle eastern population and mexican folks is strong as well with some paying triple what the stock sales bring per pound.
Free Ranged livestock is kind of hard here, we are just outside the large population center so some intense marketing could bolster sales, but as far as large livestock, not many have the room to allow them to graze without having to supplement feed. One good snow storm and the profit rolls out as the hay has to be fed all winter. Pigs are not real pricey here either, fair market but not record setting. A young 4H pig starts at $70
Chickens are about average, benefit is no restrictions on who can have them but the meat market isnt strong. People here still think store bought is the same and wont pay more for farm/free range. Closest place to me that sells eggs runs $2 a dozen and $3/dz with neither selling enough to create a profit.
I had started working the property up to raise Deer, even had someone willing to write the check for the fencing and intial breeding stock. However the CWD outbreak in one of our counties has the permit process all but stopped and no one can get a permit for the foreseeable future. With semen straws fetching big dollars from a solid Buck, the money is there.
Good luck, making money with livestock is tough but can be done!