if its practical, one of these units will give purer water than any distilled water you purchase.
distillation requires double and even triple distillation for the purest water and that still does not remove everything from the water since steam is perfectly capable of carrying particles with it as it rises from the water surface. Deionisation if far better as it actually filters virtually everything out.
But prepackaged chemicals from ILFORD etc are buffered sufficiently to allow use of straight tap water without problems. However, in a hard water area, you are likely to get drying spots on film or paper if you don't use filtered water for your last wash. And some finicky developers benefit by using deionised water when mixing stock solutions. e.g. PMK.
i.e. use deionised/filtered water for stock solution and final rinse. Everything in between should be OK with tap water unless you have very poor quality supply.