I installed a system that treats roof water to meet requirements of the EPA Surface Water Treatment Rule for public water supplies. It uses filtration and chlorination to remove suspended solids (dirt), and giardia, cryptosporidium, and other things that are present in fecal matter of warm blooded animals. Chlorination will kill residual giardia as well as viruses and bacteria.
The system consists of a two stage filter, the final stage of which is the Harmsco 1 micron absolute cartridge, and a chemical feed pump to supply chlorine from household bleach. I use the PP-BB-20-1 which fits in a 20" "Big Blue" housing. The first stage can be a standard 1 micron cartridge that costs about half as much as the PP-BB-20-1. One cartridge set costs $70 to $80 after reasonable discounts and you should get at least 25,000 gallons of water through one set. You can decrease the cost of cartridges if you use more housings.
The addition to your system would be two generic brand filter housings at about $50 each, the chlorinator (about $240), and a single stage jet pump to put it through the first stage filter before it goes to your storage tank. You should have a chlorine test kit at about $50. You will need float switch controls for the pumps. Parts for do-it-yourself installation will be less than $1000 plus whatever you need for collection and storage tanks.
You should filter before the storage tank because you don't really want to create a stew of bird and squirrel crap in your storage tank, even if it will be filtered afterward. I always chlorinate ahead of the first stage filter.
The filters will make your RO system membranes last longer. You can use a carbon filter to remove the chlorine before it goes to your RO system if you wish, but with the treated water you don't need RO.
You should have separate tanks for collection of the peak rainwater flows and for storage, unless you have a big enough pump to filter the runoff immediately. That depends on the size of your collector and rainfall rate. For example, 1" per hour on a 2400 square foot roof is 1500 gallons and 25 gallons per minute.