The most important thing is to use water that you like the taste of when it is plain. At our store location in New York, we use filtered tap water and are very happy with the results.
We do not recommend distilled water. Some minerals are necessary in the water for brewing Japanese tea with a nice taste. Since distilled water has the minerals removed from it, we do not recommend it.
Dedicated fans of tea may enjoy experimenting with waters with different levels of hardness. The hardness level of your water will produce different characters in Japanese teas. Most water in Japan is soft water, and soft water will more easily bring out the umami from our teas. In comparison, hard water will produce a more “crisp” character from the same tea leaves. So, if you like an umami-rich character, you might consider using soft water.