This could work, but sounds like a lot of work. I think there are more efficenct ways to use rain water. My grand dad is collecting the rain water for years for his garden. He doesn't really filter it and only uses it for his plants, washing and showering and sometimes for cooking. Once you boil it you kill all the bad stuff anyway. It is quite important to have a large area to collect water from. Also there are already filters you could use directly for the water.