The next question is: why would you filter tap water after it's already been treated? I'd be more concerned about the microbial population of my home filter than about the quality of the tap water in most places that have water treatment plants.
As for the juices, unlike sodas, you do get vitamins unfortunately, even without added sugar, fruits that you don't have to chew or digest to assimilate, means that you get all those extra fruit servings, without feeling satiated and without the solids slowing down the assimilation rate. It's only a small step up from sodas to juices.
My beverage of choice: unfiltered tap water.