The Need For Home Water Purification
These days, in many localities, drinking water quality is lacking because of a host of toxins that are potentially dissolved in them.  
To avoid these contaminants, such as ALUMINUM, CHROMIUM, MERCURY, LEAD, FLUORIDE, HERBICIDES, PASTESIDES, Disinfectants like chlorine, chloramine, and chlorine dioxide that can kill vitamin E and other fatty acids (that help keep your skin healthy), and a few other contaminants like bacteria and other pathogens, people resort to two prime purification methods - distillation and Reverse Osmosis (RO), with the objective of getting PURE DRINKING WATER! Not only that drinking purified water is better for your skin and helps to prevent aging symptoms, but it could also help you to reduce the risk of having major health issues and protect your family from harmful contaminants.

Water distillers and reverse osmosis systems are two methods of water purification. There is no doubt that water distillation would produce reliable clean water “While both methods remove contaminants, distilled water is purer due to the boiling process”. Still, there is one unresolved issue with home distillation devices - post distillation cleaning! Just watch this short video and see what’s left after distilling 1 gallon of tap water (min 0:40), and what it takes to clean it. Furthermore, time and again, you have to refill the distiller.
The Reverse Osmosis (RO) alternative requires far lower maintenance, and produces a very good quality of purified water at a very low price, provided that the system selection and maintenance are performed with some basic knowledge of the quality and operational parameters that determine the final results.
 
TDS - RO Water PURITY Measure
Total Dissolved Solids (TDS) Level
Asking ChatGPT "what measurement is best for water purity" - it brings TDS at the top of the list. Don't be misled by those who claim "The hard truth is, TDS is not an accurate indication of water quality". "A TDS meter will detect any charged ions in the water, which could include positively charged ions such as calcium, sodium, magnesium, and potassium or negatively charged ions such as carbonate, hydrogen carbonate, chloride, sulfate, and nitrate".

Don't be confused between water quality (e.g. water enriched with minerals + alkaline) and water purity!!! TDS is a good measure for water purity! Distilled water has a TDS of 0.5 ppm or less, so to put it simply, the lower the TDS the better the water purity! Most people who look for home purification systems are motivated by the need to remove potential water contaminants such as MERCURY, LEAD... HERBICIDES, PESTICIDES... This is the hard part (as explained below) because the size of many of the metallic contaminants is in the range of 0.0001 to 0.001 micron. Removing such particles from the water requires a membrane pore size not larger than 0.0001 micron. As an example, lead ion atoms are 0.000154 micrometers. This membrane pore size, makes it also very effective in the removal of pathogens such as Viruses that range in size from about 0.02 – 0.5 microns and bacterial cells that are in the range of 1 to 10 microns in length and from 0.2 to 1 micron in width". 

Once you get pure water - it's easy to implement the addition of the desired minerals and some alkalinity, as can be found in most water purification systems, most notably RO ones.

 

RO Systems Filtration Structure Mechanism
RO systems are actually built with two water treatment phases: ​
Phase 1 - Water purification, with a membrane filter as its last element. It is a challenge to Keep membranes with pore size of 0.0001 from getting clogged, and still provide the membrane surface area for a water flow at a reasonable rate. That is why quality RO systems come with "Auto Flash/Self Cleaning" mechanisms (Read more below).
Phase 2 - Water enrichment, adding alkalinity and mineralization. This phase is easily obtained even with some add-on filters. 
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So, how do we know what is the purity of the RO system if the water produced are enriched with alkalinity and minerals? Simple, we obtains the added TDS value of these filters and subtract it from the TDS reading that we obtain from the system's output water. Here is an example of such increase: "This filter (iSpring FA15) is capable of increasing the pH value of the RO water by 0.5 to 0.8. The Alkaline filter compensates for the lost minerals eliminated in the RO process and restores these minerals back into the pure water. These minerals being restored will slightly increase the TDS value, normally between 10-20 ppm" 

Note, a search on the web for "RO desired TDS level" would bring a wide range - somewhere between 50 to 300 ppm, saying that "TDS level lower than 50 ppm has no nourishing impact on the human body". Others claim that TDS levels in the 50-150 range, are considered ideal, hinting for the benefits of the minerals left in the water. As we explained above all these recommendations ignore the main reason for the installation of the RO system in the first place - getting clean (pure) water. Having a RO system producing output water with TDS level of 100 could leave a large uncertainty about the toxins and pathogens removal capability of that system.

bottomline - try to get as pure (low TDS) water as you can from the RO purification phase ("behind" the membrane) and then have them enriched with alkaline and mineralizing filters. If your RO system pure water TDS level starts to rise, without a significant TDS change of the input water, it's a good indication that it's time to replace the "pre-membrane" filters and/or the membrane itself .

RO System Selection
To start with, you have to decide if you look for a system with or without a storage tank.   
 

Tank Or Tankless RO System
RO system storage tank is added to regulate the water output flow rate, and eliminates the system's dependency on the system's water input pressure, without the need for a booster pump. The storage tank comes with air pressure of 7 - 8 psi which stabilises the flow of the system's output water. The main issues to be considered regarding a RO system with storage tank option are:

1. It takes space that is not always available in the cabinet below the sink,

2. Contaminants "creeping" problem. This is a problem with both, a tank or tankless RO systems. This creeping is the diffusion of ions (contaminants) through the membrane into the pure water side of the membrane when the system is idle, balancing the contaminates osmotic pressure "before" and "after" the membrane. Avoiding this problem is simple with a tankless system by letting some "pure" water flow to the sink for 5-10 seconds before starting to fill your cup. Understandably, this option is not available if the water from the membrane flows into the tank and mix with the water stored in it. Another option is to have a system that supports the auto flush feature (Read more below).

3. If there are some pathogens that somehow got through the water purification phase, be it because of inadequate filters or delayed replacement of the purification filters, and if the water remains for a prolonged period of time (9 - 10 days) without being "changed", the storage tank may become a breeding ground for those pathogens. A different source claims: "The dirty secret is: the inside of a residential reverse osmosis tank accumulates and breed heterotrophic bacteria over time. Heterotrophic bacteria are microorganisms that use organic carbon as food". The growth rate of these pathogens is a matter of "discussion", as revealed by a search on the web using the keywords "how long does it take bacteria to proliferate in RO storage tank". Still, there is no doubt that pathogen growth is an issue with RO systems storage tanks.

4. Contaminants removal effectiveness of filters and most importantly the membrane filter, depends on the feed water pressure - generally speaking, the higher the pressure the higher the contaminants removal. Most "storage tank" RO systems come without a booster pump which makes the effectiveness of contaminants removal dependent on the feed water supply pressure. That is why most RO storage tank vendors would recommend a booster pump if their system does not include one and the feed water pressure is less than 0.2 MPa (2 bar / 29.01 psi).

 

Tankless RO Systems - These systems include a booster pump that generates the right water pressure for a good functioning of the membrane filter and for "sufficient" water output flow rate - which means that tankless RO systems need a power supply to operate. Also, this booster pump and some additional electrical elements needed for its control, make these RO systems more expensive, compared with RO systems with storage tanks and similar daily water output.