I've futzed around with coffee water chem for a few years now and have my water dialed in for the coffees I prefer; lightly roasted and high acidity Africans, lactics, and S. American stuff like Geshas. Kalita and V60 pourovers. I also make a pretty good espresso on my Flair, but it can be inconsistent. That said, I generally try to keep alkalinity below 60 and limit the amount of sodium and chlorides in my water. Generally, higher ALK can be overcome by increased Ca/Mg extraction and S04. Some general findings:
Ca - heavier, creamier mouthfeel, can be dry/earthy in high amounts
Mg - crisp, smooth, highlights fruitier character
Na - bitter, flat character > 20 ppm
Cl - sharp, dull, bitter above 30 ppm
S04 - crisp, bright, dry, fruity
The principle ions for coffee extraction are Ca and Mg, although too much of either are not ideal. Sweet spot for calcium hardness for my process is around 45, and I prefer more Mg/S04 to accentuate sweet-high acidity flavors; berry, tropical fruit, ect. For darker roasts and French-Italian style espresso, I've found the opposite to be ideal; higher Ca, Cl, Bicarb for improved body and reduced acidity.
My general profile for balanced, medium-acidity coffee with good mouthfeel is:
Ca-19, Mg-29, Na-11, S04-113, Cl-16, Bicarb-58, ALK-45
All said, water does amazing things for coffee, but it won't make badly brewed or roasted coffee that much better... and grind consistency is still key.