Maybe to start you could get a barebones RO
system that is slow (10-30 gpd) and just start filling the tank with that 24 hours a day for a few days... 10gpd systems are usually under $100 especially on drsfostersmith and ebay.
Find something around the house you don't really want anymore, sell it on ebay for $100, and buy an RO
I live in the country and don't have flouride/chlorine in my water, but I do have iron and other stuff so I still get little algae "bursts" sometimes doing topoffs. I'm getting an RO
unit as soon as I pay the taxes for my truck