I used to drink filtered tap water, then switched to distilled (I have a countertop distiller), and I much prefer the distilled. The tap water in my area is very fishy so the filter helps, but then I like to distill it. Also, I distill because of the fluoride content in my city as well.
Now, it has been said that distilled water takes the nutrients out of your body and makes your teeth brittle and fall apart, but I haven't noticed any of that happening. In fact, I found that to not happen at all for me or my children or husband.
However, due to the economic downfall, when the wave of lack of funds hit us, I switched back to drinking the filtered tap water. I had noticed that my teeth had become sensitive again (they were sensitive before switching to distilled in the first place, but that went away), and so I've gone back to drinking distilled. My cooking is once again done in distilled water and I make everything with it again. My teeth are back to not having the sensitivity issues, so I can only assume that it's the tap water that caused my teeth to be sensitive in the first place. But I have heard that fluoride will break your enamel down and make your teeth sensitive. So, switching to distilled was the best choice I've ever made.
As for bottled water, I don't buy it, I don't like the taste of it, and I only drink it when there is no other option where it is available when I am away from home (like on long trips, or visiting someone).
I much prefer distilled at home water over any other source (except getting it from a natural spring directly, which there are none in my area).
That's my opinions and observations with distilled vs. tap vs. bottled.