I don't think it is so much a certain mineral that you are looking for but more of how it interacts with coffee molecules. From my limited understanding of the subject, the mineral content of the water will help in the extraction process but can also hinder it if the mineral content is to high.
The process of removal requires the use of some filtration and scale inhibitors. You how ever do not want to use a softening system for drip coffee for this will give you quite a few negative side effects.
As for filtered water, yes you need to remove fluorine, chlorine, rust, dirt, and many other things. I use Everpure products, most commonly the MC cartridge. Here's a pdf of what it takes out
http://www.everpure.com/pdf/EV961206.pdf.
They have many other types of cartridges that remove contaminates and this is what I mean by filtered water.
Now for RO water. A lot of people have read my views on Reverse Osmosis. The water quality is almost perfect if not perfect, but there are some bad qualities most people don't know about RO. RO is wasteful, in most applications you are wasting 2 to 3 but up to 4 gallons of water to produce 1 gallon of drinking water.
Next RO is slightly acidic which in the long run will eat up your equipment if it is not post treated as it leaves the holding tank. Again if it is not treated as it leaves the holding tank, RO has a tendency not to work with fill probe systems. RO water can be pure enough that it is not conductive of electricity and this is bad if you rely on a fill probe.
For people who are not familiar with a fill probe system, it is nothing more then an insulated wire attached to a tank through a fitting. This grounds the water inside the tank to a circuit. When no water is present it breaks the ground and fills the tank. Now if your water is pure enough it has no conductivity and can cause a problem.