My instinct would be filter ...

My instinct would be filter the water through sand protected by a porous ceramic, bound sandstone (perhaps held with a bentonite clay) or cementitious layer than can be maintained and cleaned. Water will gradually be absorbed and make its way through the porous ceramic, stone or slab and the sand (the clay will remain on the surface). It can then be run off into suitable storage containers/ ponds. If quality/taste is still an issue then you will need to consider running the water through activated carbon (as already suggested) after it passes through the sand. A simple, low cost and easy technique to try out. Worth a try.