I have done a fair amount of reading on this, and spent a lot of time looking for resources which actually do a good job on the topic. It's amazing to me that on something as basic as water purification, the lack of good research and writing on the topic of purifying water. Due to the pervasive influence of industry on governmental bodies, I would tend to dismiss most any advice I got from government or even the UN.
Anyway, I would suggest you read 'The Drinking Water Book' by Colin Ingram. Best one on the market right now. Ingram is an engineer, and has given a very thorough treatment to the pros and cons of all the forms of water purification, what they remove and don't remove in terms of classes of contaminants. What he says checks out with the other sources I used, including conversations with the owner of a chain of water purification stores in California who sold both R/O and distillers. His advice was that hands down he preferred distillation. Both fellows came to the conclusion that a carbon prefilter with a distiller gives the best overall results, and truly removes everything.
Briefly, R/O systems do remove a high proportion of impurities, but the membranes, being under high pressure, slowly degrade over the typical 6 month useful life, and over that time they allow an increasing amount of impurities through. They might start out being 98% effective and end up at 80% effective at the end of 6 months as larger and larger molecules make their way through the expanding membrane pore size. Some brands of R/O membranes were made using highly toxic chemicals, such as dioxins, so you need to shop carefully and know the materials they are made of and what is used in manufacturing them (traces often remain).
There is no research I have found, or that anyone else can point to, that validates these things that float around the internet about purified water being aggressive, or unstable, or leaching minerals from the body, which is the only thing that matters. Frankly I think it is either propaganda or unsubstantiated rumor. What pure water does to things outside the body only matter if you store it in plastic containers and then drink it and take in plastic,so use glass jugs. In pure physical chemistry, you would see leaching because there would be osmotic pressure. In the body, water will always have a much lower concentration of minerals than our tissues,but the body retains minerals by the action of the kidneys filtering and retaining minerals according to the body's needs. Physical chemistry and biology are two different ball games, and mixing them up is where most of this unfounded stuff comes from.
It always makes sense to consider supplementing with minerals, because our food these days is often mineral-depleted. Even water full of minerals doesn't come close to meeting all of our needs for even a few minerals we need. Organic food will help too. To me, bottom line, the small amount of minerals lost is a small price to pay for getting all of those toxins, drugs, etc. out of the drinking/cooking water. Hope this helps.