If your water is hard, or has something in it that plants don't like then RO water will help alot.. If your water is fine then it won't help much.. Rainwater is probably my favorite, but my tapwater was always fine too.. If you want to eliminate chlorine, first you need to find out if your city adds chlorine or chloramine.. If its chlorine then it will dissipate if you just let it sit for a day or so(faster in sunlight).. Algae won't grow noticably in clean water.. If its chloramine then thats more complicated.. Pet stores carry products, but I don't know whats safe with plants for sure..
I said sterile because thats usually a theoretical goal of hydroponics.. The cleaner the better, but you don't need to treat it like you're going to perform surgery or anything.. You can do ALOT towards keeping your res and lines clean by just keeping light out.. Algae love to grow when they get light..
As for the enzymes, I don't have any personal experience with the current products.. There are alot, and alot of threads on them..