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.

I use tap water (chlorinated) without incident, but if convenient (I won't boil vegetables/potatoes/pasta just to make bread) I will reuse (cooled to 95F/35C or so) cooking water if it's handy (should have some extra "stuff" in it by then - potato water in particular is a classic) or use cooled water that has been in the kettle (so chlorine should be boiled off.)

But I have no problem with using the tap-water directly. I also use milk, eggs, yogurt, nut or bean milks, beer, etc. Hmmm; I don't know that I've tried bread using coffee as the liquid - a project for the weekend, perhaps.

All work, some with more obvious effects on the results than others.

Simply use what you have at hand. All other being equal, I would resort to the same water I drink.

Bread has been baked for centuries before we started purifying our water. If you make your own sourdough (like historical bakers), the main thing is to be consistent. Always use the same water, and then you will get a stable culture. If you change the mineral content, you may change the species equilibrium in the sourdough. But it does not matter which potable water you use, as long as it is the same. OK, if you happen to have a culture whose taste you dislike, starting a new one with different water may be a good thing to try, but that is rare and not very predictable.

If you are baking with commercial yeast, it won't have a noticeable difference. Commercial yeasts are hardy little beasts, designed to thrive in countless scenarios, misused by amateurs, thrown into choking-heavy doughs, etc. Sure some conditions are better for them than others, but if there is any noticeable difference, it will probably be that the yeast with the suboptimal water takes a few more minutes to rise. And these fluctuations in rising time are small when compared to fluctuations caused by other factors, so you have to rise your dough until ready anyway.

Only if you have an unusually impure water, and/or notice weird smells in your bread (and know they are not caused by some of the more common reasons like thiosulfates or ammonia from wrong rising speeds) is it worth changing your water. Maybe also if you are a high-volume artisan baker and have all other variables of the process perfectly controlled and are now finetuning the last details. But for the normal home baker, tweaking the water is unlikely to give you any returns on the invested time.

I think rumtscho, above, said it well, as to your question on water. However, it is recommended that if you have tap chlorinated water to let it set out on the counter for overnight, to let the chlorine evaporate.

When I thought I had 'killed' my starter, I looked back to see what things I had changed from one day to the next, and realized one item that I did differently was, in a moment of haste, I used my well water. I had also used a metal spoon, and I think I had reduced it before it was strong enough to survive that.

I have not yet totally gone off of bottled water, but am now adding 1/2 well water, after letting it set on the counter to warm up to room temperature, as our well water is very, very cold. I guess I'm doing as rumptscho suggested: bakers only recently have had 'purified' water, and I am introducing my well water a bit slowly, as it is quite hard water.