Personally I would like to get the chlorine out before I drink the water, but then chlorine has keep many of us alive who would be dead long ago with it. The amount in water by the time it reaches you home is very very low and has been shown to be quite safe. In fact it makes most filters safer since it help kill the stuff that grows in the filters if someone does not change them often enough. It also is not easy to get out using filters (so I understand)
Fluoride in the quantities it has been added to water systems has been found to be beneficial and is a naturally occurring in many water supplies. Not to mention it reduces tooth decay.
If I still have your attention, congratulations. The above aside, it should be your choice.
I might suggest you may want to re-consider that bottled water. It has been found that those plastic containers add some far more harmful contaminates to the water than the ones you are worried about. Not enough to kill you and unless you leave the water sitting in the jugs for extended times they should not hurt you, but I would rather not have it.
All filtering systems have their good and bad points. I would never ever trust the web site run by or paid for anyone who would benefit from the sale of the product. You are right to be confused, after all they don't want to inform you they want to sell you.
I suggest taking a look at the most non-commercial test you can find. Consumer Reports magazine is a good source, at least it is if you read the whole thing to understand how they do the ratings. Too many people only want to read the final results and then don't understand what they mean.
Good Luck