You’ll generally find onions offered in four basic varieties: yellow/brown (same name for the same thing), white, red and sweet. Yellow onions are generally the cheapest, and have the strongest flavor. They're pretty overpowering raw, but cooking mellows their flavor nicely, and their inexpensive price makes them a fab choice for most of your cooking needs. White onions are a little bit sweeter and less pungent than yellow, as are red onions. Red onions, in particular, are great either raw (on salads or sandwiches, for example) or grilled. Slow cooking them, however, ruins their best feature, that gorgeous purply-red hue. 

Onions that are labeled as sweet onions can actually come in a variety of colors (generally yellow or white), and are distinguished from other onions in that they have a much higher water content and a much lower sulfur content (which is what gives onions their pungency). Maui, Walla Walla, Vidalia, and Spanish onions are all examples of sweet onions. They’re good raw, or lightly cooked, but tend not to keep as well as the stronger onions.