No matter which goat I drink the milk from it tastes goaty to me. It also upsets my stomach.
I haven't had the same problem with sheep's milk as with goat's milk.
East Friesian and Icelandic sheep are the most popular breeds of sheep that are precisely for dairy. They are also more readily available than other dairy sheep. I've found that the hair sheep, Katadhin and Barbados(Black Bellied Sheep), tend to produce a fair ammount of milk and are quite meaty. Polypay sheep are a good dual purpose sheep and are a breed created by crossing a dairy breed, a wool breed, a meat breed, and Finnsheep which are known for multiple births. They have a good production of milk and also produce a bit of meat to go with.
For a year round production of milk you would need to breed back your ewes in order to have two lambings per year. This can be done about two weeks after the ewe lambs when she comes into heat again for a short time. Hair sheep breeds tend to be more prone to breeding year round than other breeds of sheep.
I personally raise Finnsheep crosses and they produce a fair ammount of milk, but the multiple babies tend to use all of it up.