Boy there sure are a lot of opinionated people here on the subject of H2O. First of all, to dispell some myths....
1. Water is not what causes kidney stones. There are different types of stones that form for different reasons. Some form from calcium, which is a mineral not often found in water, but which is also something your body needs. Go ahead and try to boycott calcium and see how long you can go without losing teeth or breaking bones.
2. Getting plastic from the containers... while I'm sure a few parts per million are going to be plastic, you could make this argument about literally anything. I drink soda pop out of an aluminum can. I wonder how much dust and even traces of aluminum I'm getting! WHO CARES?! And to say that tap water is better - no. Tap water is usually fine, and cities treat tap water - but you're also running tap water through miles of copper and plastic pipes, some of which may even be corroded. So while it's virtually the same as drinking bottled water, it is NOT better for you.
ANSWER: go with bottled, distilled water if you're really worried about getting the healthiest water. While Captain Plastic will tell you you're getting bottle plastic in your diet, it doesn't really matter, and you're getting the purest water available. If you're going for taste, try a brand called 'Fiji' which is bottled in the island nation of Fiji, and which has some minerals in it, and tastes clean and nice.