I guess the thing that confuses me about this question is we must assume that all "natural waters" are not drinkable. That is not really the case as some well waters are actually relatively pure and good for human consumption right out of the ground. Of course there is no way of saying a well will never become contaminated by some down stream source, so as a precaution some sort of disinfection would be recommended.
Yet, if we examined water at the molecular level we would have to come to the conclusion that it may not be the best liquid for human consumption as pure H2O. Water that is ultra pure tends to be very aggressive and has been called the universal solvent. Drink pure water and lose a layer or two of your intestinal wall. No thanks! So, a little bit of "stuff" in your water is actually good for you.
Best treatments for making natural water drinkable depends upon the chemical constituents of a given water supply. A source with pathogenic contamination would need disinfection along with filtration. However, the first recommendation would be to find the source of the contamination and remove it.
There are also the issues of radiological, heavy metals, arsenic, organic, iron, manganese, hardness, TDS, dissolved gas levels with each having a best available technology (BAT) for the process of treatment. If chlorination is used as a means of disinfection then trihalomethane levels have to be considered. Carbon filtration is usually recommended in this case as a means of removing free chlorine and the by-products chlorination creates. UV is an alternative means of disinfection, but the water to be treated must be clear. Filtration with a multi-media backwashing filter is usually recommended as pre-treatment before the UV system. The down side of UV is the fact of no down stream disinfection properties of the ultra-violet rays.
For iron and manganese contamination there are several ways of removing these contaminants. For high levels - Chlorination/oxidation/filtration, moderate levels - greensand filtration periodically regenerated with potassium permanganate, low levels - ion exchange.
Most aesthetic issues can be treated with ion exchange and reverse osmosis. So the best treatments typically depend upon the contaminants and the end use of a given water.