This is by no means an exhaustive list of the available breeds of sheep. For a complete listing of breeds with easy to find factual information the best resource is Storey's Illustrated Breed Guide to Sheep, Goats, Cattle and Pigs written by Carol Ekarius.
When you are trying to pick a best breed, recognize that there are always trade offs. The goal is to pick the breed that reflects what you wish for or need the most.
Almost as important as selecting breed and perhaps more so is selecting the right type of animal. The right type of animal might be a cross bred of two of more breeds. Selecting the right type of animal will give everyone a head start as the animals will be more likely to perform well in the environment you raise them in.
Breeds of Sheep Suited for Grass Based Sheep Ranching
The breeds listed here are noted for their ability to perform well in grass based operations or on range conditions.
Columbia
Rambouilett
Targhee
Katahdin
Clun Forest
North Country Cheviot
Corridale
The desirable traits that make these breeds good candidates for a grass producer include:
Hardiness - able to maintain body condition on grass alone, do not need supplemental feeds to perform well
Efficient on feed - they eat and maintain condition versus eating to become obese
Lamb without assistance - good maternal skills, know which lamb is theirs and often birth lambs with good vigour (get up and go)
Raise a lamb on grass - the ewes are very capable of raising their lambs without requiring supplemental feeds. The lambs grow well and thrive on grass as well
Breeds of Sheep Noted for Maternal Traits
It is a good idea to keep in mind the breeds that show a tendency to have strong maternal traits since one or more of the maternal breeds will often make up the breeding animals in a flock.
The the maternal breeds will express characteristics such as strong bond to lambs, will keep track of their lambs and keep them close by, lamb easy, attend to newborn lamb immediately, good milkers (not heavy milkers necessarily), raise lambs with vigor.
Columbia
Merino
Cheviot (Border and North Country)
Dorset
Polypay
Rambouillet
Targhee
Breeds of Sheep Noted for Terminal Sire Traits
Terminal sire animals are used for the purpose of producing a market lamb. The focus here is on the frame of the animal and weight of gain. The female offspring from terminal sires are not usually kept on as replacement ewes as the qualities sought for replacement breeding animals are not those expressed by terminal sires.
If you are in the early stages of building your flock you may wish to build up your maternal qualities to grow the foundation of your flock and then focus on terminal sires for producing market animals.
You also have the option of splitting the flock and using different rams for the two purposes. You would place a ram of the maternal breeds with your best maternal ewes and keep the best replacements from this group. For the second group you would select a terminal sire breed for a ram and then market all the resulting offspring from this group.