This is one of the least understood areas of coffee, by the coffee retailers. I have been looking into this for my own shop and there is some good info out there, but it is not what I would call a "mature" subject, in the way that espresso temperature, pressure, bean roast, etc. are.
Yes, you do need minerals in your water. Filtration will not take them out. Nano filtration and reverse osmosis will. RO can strip it back too far. Softeners take out the scale, but replace it with sodium. Antiscaling systems inject phosphates into the water, reducing the ability for scale to form.
For home use, a good sediment and carbon filtration system should be sufficient. Especially for brewed coffee. If you are making lots of espresso, you might consider doing something to reduce or inhibit the scale. The boilers take the hit on scaling up.
Cirqua offers systems that "re-formulate" water. For a few thousand and up, they will filter, RO, and then remineralize to targeted Total Dissolved Solids (TDS - hardness, scale) and ph.
Ideal TDS for brewers may not be ideal for expresso machines. I'm still working on this one, and on my own system design. Input that I have collected:
sodium - bad for taste in ice
scale - bad for espresso machine, bad for ice machine and flavor of ice
scale - needed for proper extraction of coffee
polyphosphates - bad for me, Cirqua calls it bad, but that is competitive marketing. popular technology, approved for use in food, no objective input on flavor available, but I don't want it in my brew.
RO - good for ice, pure RO can etch equipment over time, e.g. boiler.
Articles in FreshCup, other trade magazines are marketing platforms for the equipment suppliers. They do provide some good targets on TDS, ph. But no solutions other than their advertisers.
I have to say that Cirqua knows their stuff and this industry. I have been very impressed talking to them, but the pricing is high. Culligan can do the same thing, but did not know the business, and the pricing is high. Local water treatment shops thought I was crazy, "You want to take the minerals out and then put them back in? ...."
I currently have a system on the drawing board with under $1000 in parts that can provide over 500 gallons reforumlated water per day. Way more than enough. I haven't built it yet and, what scares me most, is that I have not had to maintain it yet. One mechanical item is rated at 100gpd, and I will be placing a heavier demand on that. Still trying to find out what the design factors are that give it the 100 gpd rating.
Here is probably the best document that I have found on water. Several pages, exhaustive detail of what and why. If my system works, it had better or that Cirqua system goes up by the $1000 wasted, I'll post it.
If anyone else has some definitive answers, please let me know. What I have is only opinions and conjecture obtained from articles and other postings.
Charlie