Japanese recipes often use sake for Japanese cooking, because it increases the flavor of food, removes the unpleasant smell of fish, and tenderizes meat. But unlike wine in French or Italian food, Japanese food doesn’t require expensive sake. Rather, Japanese chefs say that cheaper one is better for cooking.
One of my neighborhood liquor store increased their inventory of sake, as demand from Americans increased. No wonder that as Americans eat more Japanese food, they also drink more sake. But sake you can get in the U.S. market tend to be too delicate and expensive to use for cooking. The one you want to use for for Japanese cooking is affordable 1.8 liter bottle, which is also good to drink.
Japanese grocery stores carry cooking sake, which is much cheaper than you buy at liquor stores. But it includes salt in order to avoid alcohol tax. You could use it for cooking, but if you do, you have to use less salt, soy sauce, or miso to avoid making the food too salty. Alternatively, you can brew on your own in 3~4 days.
Mirin and sake are used for different purposes and are not interchangeable. Mirin is used to give glossiness to food, but sake is used to increases flavor, removes the unpleasant odors, and tenderizes meat.
Sake can be found at liquor stores. I believe Chinese liquor or Korean liquor tastes different and is not for Japanese cooking.