purified water has as much as is possible to remove from the water (based on the process)
Reverse osmosis water has pretty much everything removed.
sounds good so far right ?
it has no minerals, it is completely sterile, it has nothing that can be of use to anything in your tank.
kinda like breathing pure O2 (you would die of asphyxiation as your lungs dried out)
similar to excessivly purified water.
Tannis/tanin (often from wood) will lower pH. i don't know what it tends to try to push for (before other buffers in the water reach a mutual balance) i have looked to find what the pH is of tanic acid, ... i am still at a loss, i gave up, ... but it is known for lowering pH ... good for certain fish.
many minerals that are present in water will have their own preferences on desirable pH (calcium wants to make the water about 8.4 i think.
chemistry here is ... enough to give you headaches
a high pH phosphate will try to bond with calcium in the water, removing phosphate (which is usually limited to begin with) and leaving enough calcium to still want to keep the pH high
life is a struggle isn't it
mineral water 'should' be good, ... i am no expert at all on water, ... i should look into that actually.
all i have seen for 'healthy' water purifiers amount to purifying the water, then adding their own intended minerals to the mix, (looking at redox here - another chemistry thing

... based on human health, ... all of our anti-oxidant hype and propganda are related to this.
they have found (for humans) that a natural pH that is slightly higher than 7 (i don't know what the goal is, 8.4 sounds like the magic number - although it's more of a range) to bring the body to a state of the right oxidizing potential & resistance balance for our health.
now putting 'human health' aside (we don't live in our tanks)
our fish have their own desired pH range they want for their health. the idea is the same though, and there is enough general knowledge around for each fish species out there to know what the optimal range is
it's also known that stability is more important than a set pH number, as finding your tank at 8.0 when your fish are happiest at 6.7, ... and suddenly changing the tank to 6.7, ... well you'll induce shock to your fish at a sudden change where the fish (while not happiest) have adapted to your current pH, ... so long as it's stable.
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as for what kind of water to use. the topic at hand.
the million dollar question.
i'm a little paranoid, not good. and i worry about heavy metals. and other toxic levels.
aluminum isn't healthy but i have red plants can benefit from some aluminum present as it bonds with heavy metals. (higher levels it's just toxic)
copper is another good one, in low concentrations, higher concentrations it's just toxic
lead, pretty sure it's toxic at all levels
uranium well we know this isn't good for anything ... and yet average human elemental compossition estimates we may have a few atoms of these in our bodies, largly undetectablely low levels, but i red somewhere it can be expected to be present (if only a few atoms)
these are all minerals that may be present in water, "MAY" not "IS" and while what comes to mind as 'well water' may be perfect as it's high in all the micro-nutrients and minerals to help things out, it's also completely uncontrolled.
mineral water is (i am assuming here) what is bought from a store, ... either collected from a stream and filtered for water clarity & sediment, ... or purified water that is then mineralized with whatever the company decided was appropriate.
(don't you like our aquariums, no end to what to learn and how far you can go in learning, ... yes, that headache again

it's not simple damn it
back to that human healthy water
https://santevia.com/
great for fish that want a high pH
otherwise i can only think of this as a place to start and is something you can own to purify your own water.
it's a place to start if you want to get paranoid and tinker with your water too much.
otherwise, you can go simple.
-the more expensive side (buy mineral(ized) water from the store - make sure without flouride, that's a toxic marketing blunder too much of the public believes is good for your health
-or the cheaper tap water (there is usually enough additives to the water to reduce lead & copper from being present - this is intentional as it's cheaper to add these things to the water to reduce lead and copper from eroding/corroding from the city water piping infrastructure to ensure they last longer (repairs can be expensive)
while i don't know for certain, ... my guess is these additives amount to phophates and such things that are not inherantly toxic and could be more on the beneficial side of things.
the additives taht are toxic are usually intentional ... call your municipal water company and inquire on chlorine/chloramine/flouride additives (and you can take appropriate measures if your concerned.
on the whole, ... thousands of fish keepers use tap water from all kinds of areas with all kinds of treatment options and for the most part their tanks do rather well
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so ...
depends on your level of paranoia
depends how much you want to spend
depends on what your fish preferences are.
above all, regardless, ... stable is always better as things drastically different from your tap water can cause fluctuations with your tank water
again that's the more paranoid side, ... your tank water will more likely have it's own dissolved solids and natural buffers in place to keep your water parameters stable with all but the hardest tap water you would be using.