Go with a reverse osmosis system. Takes out all sediment, chemicals, bacteria, viruses, heavy metals etc etc to a level of 99.99%. Its the only way to go.
Apart from the fact my business markets and maintains these units (so yeah I'm biased), they simply are the most thorough and efficient. Here, the tap water is chlorinated, fluoridated - you name it, its in there. The human body doesn't need chlorine - its been linked to heart problems over long term consumption. And we get way more than enough fluoride just through brushing our teeth and other means every day.
For people with rainwater tanks, we tend to use an Ultra Violet light to run the water through to kill off the nasties in the water, and some also like to then put it through the reverse osmosis filter (4 stage unit - sediment filter, carbon filter, reverse osmosis membrane, into the storage tank, then out through a taste and odour filter to your sink top faucet - this increases the pH to 7.5 from 7 to make it a tad sweeter to the tastebuds).
Plus it tastes so much better - food tastes better cooked in it too.
I can sell you one for a special price ;) hehe j/k