My theory is if it is safe for drinking then it is good for brewing. Your water profile does give your beer uniqueness. It’s like the whole Rolling Rock move, people were upset we they moved the brewery from Latrobe, PA because part of what made Rolling Rock "Rolling Rock" was the water in Latrobe. This lead people to believe that the beer would suffer. The ironic part is most people say it’s now better than before (go figure).
With all that your water should not have high enough levels of chlorine and or chloramines to cause extreme off flavors. Having been in the aquarium hobby for quite some time, both of these always pose an issue. Chlorine can be remove simply by letting you water sit for 24 hrs (a little sun light will help), as chlorine evaporates quickly (boiling the water also works). Chloramines is another issue, they do not evaporate which is why most public water systems now use them. High levels can lead to a metallic taste in the beer, which means you should avoid brewing for a week after a system cleaning is done, because the levels of chlorine and chloramines are increased to clean everything. Water companies do this about every 6 months and you can call them to find out the schedule. Chloramines can be removed by increasing the chlorine to over 10ppm, which in turn will break down the Chloramines allowing it evaporate along with the chlorine (I would let the water sit for a few more days and boil prior to use). If you use campden tablets make sure they are potassium metabisulfite, because the sodium metabisulfite ones can also lead to off flavors from the residual sodium left behind.
In the end I have never worried about it, straight from the tap to the brew pot. If you are concerned about the levels some pet shops do sell test strips that can detect low levels of these chemicals for a fairly cheap price; however the scale usually does not give ppm.
Distilled water is another story. Most people think it taste funny, and that is because it has no taste. The minerals in that water are make water taste like, well water and if we remove the minerals the beer will suffer. So if you use it you must add minerals back in like stated earlier; for flavor and the yeast will also need the minerals as micro nutrients. You should not even drink large quantities of distilled water because if can cause your electrolytes to drop to dangerous levels.
Brew, Ferment, Package, Drink, Be Happy!