What is the best water to use for yeast being used in bread making?
There's no single right or wrong answer to the question as it depends on the mineral content (ie hardness), acidity, and chlorine content of your water. Yeast and gluten development is affected by these factors, see this good summary from the King Arthur Flour site:


  The degree of hardness is an indication of the amount of calcium and
  magnesium ions in water, expressed in parts per million (ppm). Soft
  water has less than 50 ppm, while hard water has over 200 ppm.
  Generally, water of medium hardness, with about 100 to 150 ppm of
  minerals, is best suited to bread baking. The minerals in water
  provide food for the yeast, and therefore can benefit fermentation.
  However, if the water is excessively hard, there will be a tightening
  effect on the gluten, as well as a decrease in the fermentation rate
  (the minerals make water absorption more difficult for the proteins in
  the flour). On the other hand, if water is excessively soft, the lack
  of minerals will result in a dough that is sticky and slack.


Acidity has an effect as well, too acid or too basic will impact your yeast, neutral or very slightly acidic is best. 

Water with a high chlorine content is not ideal as it may impact the flavor of the bread, and can impact the development of cultured starters like sourdoughs. Chlorine is not an issue though as simply leaving water in an open container for a day or two will let it naturally disperse. 

So, your bread will be best if there's some minerals in the water to feed the yeast and aid gluten development, it will also be best if the water is very slightly acidic. In many places water that comes out of the tap is perfect, and in most places it will work fine. Purified water is not good because it doesn't have enough minerals in it. Filtered water from a RO system may be fine, whether you want to go further really depends on how much residual mineral content there is in it. I live in a hard water area, about 250ppm, and I use a brita filter for my bread making and cooking and as long as the filter is not used up it seems to work, although I don't know what the actual mineral content after filtering is. If I really wanted to know I would get a testing kit, they do not cost much and are simple to use. I would suggest you get test kits for hardness and acidity, you probably don't need one unless you know you are adding it in your RO system. 

Another good article I've seen on the subject is here.

EDIT: chloramines
Chloramines are sometimes added to water instead of chlorine because it does not evaporate easily and therefore much less can be used. The EPA's guidelines is a maximum of 4ppm, however beer brewers state that yeast eating chloramines can produce off flavors in the end product even in small concentrations. I don't know how that translates into bread baking though. Chloramine can be boiled off, but that takes a lot of energy, or you can use Campden tablets to remove it. A charcoal filter like a brita can also remove some, how much I do not know. All I can say is that I've never detected any off flavors in bread when I've used filtered water.