Keeping livestock takes commitment. If you are considering getting a cow or goat, you should prepare for what it might mean. Getting one of these animals is not simply a "making my own milk" kind of thing. It means committing to owning an animal. Besides this, as Wayne Fajkus pointed out, if you want milk, you need babies. That means besides that doe or cow you want, you're going to buy or rent a buck or bull to breed it with. You'll need to research and ask around to find a reputable herd to get a buck or cow from so that you won't get a buck who is unhealthy and will get your doe/cow and the babies sick. Now you have a buck/bull on your hands, possibly permanently. You also have to pay for the costs of breeding your goat or cow, such as a vet if you are inexperienced with birthing animals. Then after the birth, you have a young animal on your hands. For cows, generally there will only be one baby, but there could be a possibility of more. For goats, twins are most common, but triplets are not uncommon, and quadruplets are always possible. Will you sell them? Eat them? Keep them? For any possibility, you should consider your breeding options to fit your intentions.
Most likely if you want a good quantity of quality milk, you will start a herd, which takes a good deal of commitment. With that said, there is the dispute between goat or cow.
I myself am partial to goats. They are reasonably easy to care for, don't smell to much, easy to walk, don not require a great deal of space, and don't eat out of house and home. Cows are extremely smelly, large, leave a huge mess, not so easy to walk, and eat a good deal more than goats. They also need a larger place to roam.
That being said, cows do produce more than goats, and provide broader options no matter the kind if you do not wish to keep the babies. Goats are also needy. They need to be loved and cared for, and a larger herd is usually best so that they have company.
As far as quality milk goes, I would say that neither goats nor cows have better quality.
So as far as goat or cow goes, it depends what conditions suit you best. Just know that no matter what you choose, you must be prepared to work hard.
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