Wen My aunt lived in a house that had a cistern-- which collected rainwater from the roof, the only treatment' the water received was to go through a filter to remove those grains of whatever that are [part of the shingles, and any larger debris that may collect on a roof.
However, if you go to a outfitting store, like Gander mountain, onecan purchase water filters that will filter the tiny micro-organisms out-- like cocci, giardia, etc..
If you want to go further, 1 tsp of tincture of iodine in a gallon of water ' purifies' for bacterial agents. REAL 'Clorox' ( Chlorine based bleach, not oxygen) can be used at a higher concentration to purify drinking water for people-- I remember having a chart on hand when I lived in Florida-- part of the 'Hurricane Kit'
vanilla flavoring, whether'real' or artificial can be used in water-- 1 tsp per gallon, to kill aspergillosis-- a fungus that is in the environment. this works by changing the pH of the water -- I suppose vinegar would do the same...