Mineral water from a glass bottle can have a good taste, is clean and does not contain fluoride (or far less than tap water).
It is sodium in mineral water that is most responsible for its (good) taste. Different brands contain different (small) amounts of sodium, mostly in the range 50-200 mg/liter.
You do not need to seek for "healthy minerals" (calcium, magnesium) in water because you usually get them in greater amounts from foods.
Here on USDA is a list of about 100 brands of mineral waters with nutrition facts, here is one example: 330 mg Ca, 110 mg Mg, 130 mg Na per liter.
Distilled water contains no minerals, so it does not have any taste. Reverse osmosis water is pretty much the same.