My tap water in Vienna is hard enough to make about a 10% difference in my developing times with PMK as opposed to those in Oregon, where I have very soft water. There is a similar, but lesser affect with other developers. The tap water works fine, but I do have to compensate for the added activity of the developer. If you are just working in one place, this will be just another of those personal variables we talk about so often here. If you develop with lots of different qualities of water, then either test for different times or standardize on bottled/distilled water.
That said, I simply use the tap water for dilution and all working solutions and washing up until the final rinse with Photoflo, which is done in distilled water. It is not a question of "optimum" water quality, but rather whether the water quality has a detrimental effect on the processing. Often, it doesn't However, I have found that final rinses with hard water can leave mineral stains (if you have a water softener, you may get salt crystals...). That's why I use distilled for the final rinse. I imagine any good demineralized water or filtered soft water would do as well.
Note that many stock solutions are better mixed with distilled water, due to the differences in solubility of chemicals in near-saturated solutions. I once made the mistake of mixing PMK B-solution with the Vienna tap water.... not much of it went into solution. I had a liter bottle 1/3-full of precipitate.
Hope this helps,
Doremus Scudder
www.DoremusScudder.com