So, I was on a dummy for most of my coffee drinking life. I used tap water when it didn’t smell or taste bad (which is ok to do) . I have however, used distilled water on many occasion.
Distilled water tends to throw the fine taste of freshly ground coffee bean out of whack. You should only use clean tap water or a quality spring water if you want to reach peak flavor.
I can not be certain if purified water has the same effect that distilled will but I would be willing to bet it would. Personally, I’ve always enjoyed my cups brewed with distilled but that is what the experts recommend.
Since we got a water purification system on our rural well water, coffee has been simply heaven. I highly recommend going that route if you can afford it.