Quality of Garlic

Garlic lasts a long time, how long depends partly on variety. Hardneck varieties have fewer, bigger cloves and generally do not last as long, softnecks have more and smaller cloves and last a bit longer, but they both last a very long time. I grow garlic and I'm usually still using my last year's batch when my next is ready, so you should be able to keep yours for weeks at least. If it is sprouting most likely you are storing it in the refrigerator, this is a common mistake as most people do not know that garlic germinates in cold weather. Store it at room temperature instead.

I've lived many places in the world and there's no single answer to the quality aspect as it varies from place to place. In most of the US and UK the garlic you get at the supermarket is pretty tame, bred for quantity over quality, whereas in Italy and France the garlic you get at the supermarket is far stronger - one clove of Italian garlic is equal to a whole bulb of typical US supermarket garlic. Organic varieties in supermarkets tend to be much better, you can also order online if there are no good local farmers markets or other sources nearby.

If you like good garlic and you have the space you could grow some yourself, that way you can pick a strong variety. It's actually very easy, tolerant of a variety of soils, you just need to make sure its well fertilized and not to let it get dry. Of course, depending on where you are in the world it may be too late to plant out as it needs cold weather to germinate.

I can back what GdD says about US commercial garlic. Until recently, most was grown in California, now much comes from there, Mexico or further South and it is a variety known as California White. It is a mild, mass produced variety that is grown in a climate that is easy to grow in, but poor for garlic quality unless you like mild, bland garlic. If you want potent stuff, it needs to over winter in cold weather but not cold enough to kill it. About the only heavily grown stuff around here more mild than California White is Elephant garlic, which is actually a leek, not garlic.

However, there are many varieties that are much more pungent, especially if they get a nice winter chill. Many hardneck varieties have much stronger flavors, and nice big easy to separate sections, but unfortunately have the shorter shelf lives. Some Polish varieties are some of my favorites when I lived where I could grow them because they were flavorful, and nice looking with purple and red paper, but many of the European and Amish varieties in the US are nice if you can grow them yourself. They actually are pretty easy if you have a little room and patience. Farmers markets are always a good bet to be able to find varieties and often you can get smaller quantities like 2-3 heads.