Bernstein and Willox in "the practical brewer" stress the importance of the choice of water in brewing beer. It is well known among beer brewers that some types of beer require precise kinds of water. But there is not such a thing as a famous mead and its associated water. Other criteria will have to be found.
The cheapest water is tap water. Unless it is bad to the point that it cannot be drunk, it is more simple and less expensive to use the tap than to buy spring water (ask the city water department to get information). Boiling tap water for 10-15 min before using it is a good way of getting rid of some of the chlorine it contains (but it takes some time for the water to cool down and one has to keep in mind that more than a quart of water must be boiled to eventually get a quart). During fermentation, chlorine could be turned into chlorophenols which tastes like plastic [B1].
There are enough different honeys and yeasts not to try and use some awkward water. If one gets a good result with some honey-yeast combination using tap water, it is possible to use the same honey and the same yeast with various fancy spring waters.
According to H4, water must be chosen to match honey: a low minerals water and a honey with little ashes (mineral matter) may not provide the minerals yeasts need. On the other hand, a high minerals water will not fit a high ashes honey.
B1 gives a rather complete list of minerals found in water, including their effects on flavor and fermentation.
Demineralized water -- containing no minerals at all -- is to be avoided.