I would not give a baby or child distilled water because there are missing minerals, such as flouride.
If you have city water it's fine to give tap water, but I would at least use a home filter to filter out bad chemicals yet still keeping in the flouride molecules.
You can use the special infant water that is sold in stores, but it's pricey and I think the only difference is that it's filtered water - basically cheaper if you did it yourself with a Brita or other home filter.
Or you can always boil the water, but it's inconvenient and "kills" the minerals in there plus babies need to start building immunities and all that.
HTH