Most folks store their milk in a single plastic gallon jug in the refrigerator. When it's nearly empty, they buy another. When you produce milk on the homestead, storage is very different, and presents a few challenges.
I keep milk in glass jars to prevent any "off" taste passing from a plastic container. Opaque is best, but glass is clear by nature, so we just deal with that. Glass is much easier to clean than plastic.
Last year I bought half a dozen half-gallon size canning jars to store milk in, then realized that they are too tall for my refrigerator shelves. So, I went back to using quart-size jars. They don't hold as much, but they do fit better in the fridge.
That means I have several quart jars of milk from each day's milking. Keeping everything straight in the refrigerator can be tricky. My system is working pretty well for us now, so that we know which milk is the freshest when we reach for a jar.
When we had our first goat, we bought plastic lids for the canning jars, which came in white only. Along the way, I've collected lids from mayonnaise jars, some brands of peanut butter jars, and other sources. Some brands fit the canning jars better than others, but you learn that as you go along. They come in several colors, and that is the secret to my system.
Each day I use a different colored lid, for example, today might be green lids. Every jar of today's milk has a green lid. Tomorrow I might use red, then blue, then white, then start over again.
And each day I move the milk jars to the left on the shelf. My family knows that the jars on the right are the freshest (or rather, they should know that. Sometimes I still am asked, "which jar am I supposed to use?") All of today's jars, with matching lids, are on the left side of the shelf, in a row. Yesterday's milk jars are in a row, just to the left of today's jars. We have one refrigerator shelf dedicated to just milk jars. (I have friends who have entire refrigerators dedicated to milk storage.)
We use the freshest milk for drinking. Since we have an ever-renewing supply - except in the winter - we might as well drink the freshest. Day-old milk is used in cooking and cheesemaking. Excess milk is frozen for soapmaking or given to the dogs and cats and, if we have one, the pig. My chickens aren't excited about milk or whey, but the dogs and cats go crazy over it. (I have to lock the cats up before I milk or they will help themselves!)
The lids go in my dishwasher when the jars are empty. I put them in mesh bags on the dishwasher's top shelf, and store them in a gallon-size jar until I need them again.
PS - Check out the Comments for more great ideas.