Any of the dairy breeds will be good for milk, so I'd recommend looking around locally, either for goat breeders, or on Gumtree/Craigslist, and anywhere else you'd find livestock for sale, and seeing which breeds are available.
Different breeds can be found in different countries, here in Australia the most common dairy breeds are Saanens, Toggenburgs, British Alpines, and Anglo-Nubians. If you look up a dairy goat association for your country or area, you will find a list of the dairy breeds there.
Anglo-Nubians have a bit more meat on them, but they are noisier than Saanens, Toggenburgs, and Alpines, so whether Nubians are a good for your yard or not will depend on how close the neighbours are.
Another consideration is ease of handling. Saanens are more predictable and easier to handle than other breeds. People with less strength often consider dwarf goats such as Nigerian Dwarfs, because the smaller size makes them easier to handle. I have no problems with handling full size goats by myself, but some people do.
I would not recommend buying goats from Craigslist or the sale barn in the US. Maybe this doesn't happen in other countries, but I've heard too many horror stories of people buying sick goats from those places in the US. There are some goat diseases that don't have outward symptoms until it's too late and then your whole farm has been exposed. For example, Johnes lives on pasture for about five years, so you would not be able to bring in any sheep, goat, or cows to your farm for five years if you had an animal with that disease. Here is more info on that:
The breed you get really depends on whether you want a quart of milk a day or a gallon or two, as well as how many goats you want to have. Keep in mind that you must have at least two because they are herd animals. Alpines and Saanens are for those who want gallons of milk every day. Nubians give a little less but have higher butterfat. The highest butterfat is in Nigerian dwarf milk, but they only give a quart or two a day. Here is more info about Nigerian dwarf goats:
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