There are two ways to purify your water. You can run it through a filter. Or, if you want the purest water possible or your water is extremely nasty, you can distill it. The best countertop water distiller is the MegaHome White Enamel with Glass Collection.

You just plug it in, pour in the tainted water, and four hours later you have a gallon of absolutely clean water. It boils your impure water and condenses the clean steam. It's also great for filling devices like clothes irons that need distilled water.
It also comes with a charcoal filter, but many users say this isn't needed. It's sturdy and well-made, and can produce 4 gallons of very pure water a day. And it's easy to clean.

Distilling water is the safest way to remove bacteria and other impurities. Countertop water distillers boil water and condense the steam, so they're fairly slow and energy-intensive, but they work well. The Waterwise 4000 Water Steam Distiller with Glass Jug does the same fine job as the top rated MegaHome Countertop Water Distiller.
It has similar sturdy steel construction, and a similar profile and design. Both have a fan noise that is bothersome to noise-sensitive users. The big difference is that the Waterwise costs $100 more.