Reverse-osmosis based systems are the current best, cheap and, well, pretty much the only ones available on the market, since it's the cheapest way to purify water. But they have a learning curve, require quite a bit of maintenance and waste some water. Although I believe you can trade wear out of the membrane for less water waste, if water is too expensive in your region. The most basic system costs like $100, has at least five filtering stages with three different cartridge replacement rates and likely needs periodic chlorine disinfection. You can add other stages afterwards: mineralization, UV, etc.