I have a 1 gallon countertop distiller. After distilling, I pour my water through a Zerowater pitcher for taste. I have 10 BPA-free plastic jugs that I pour my distilled/filtered water into afterwards. That's my setup. I did some experimenting years ago and this is what works best for me. When I see and smell the 'crud' in the bottom of my distiller after it finishes a gallon, I am happy I spent the money for it. The odor is horrible.
This way, I get water that reads zero ppm and my Zerowater pitcher filter lasts forever since the distilled water has 1 to 2ppm (extending the life of the filter due to less crud to filter) and my water tastes great. Also, when times are crazy and folks are snatching water off the shelves at stores in a panic, I'm at home doing business as usual. I fill up my 10 jugs and I'm good.
Sometimes I add a few drops of electrolytes to my water when I pour a glass and sometimes I don't. Just depends on how I feel and honestly, the taste is great without the electrolytes, but since I am fairly active, I use a few drops of electrolytes perhaps once or twice a day.
My tap water is pretty good measurement-wise ~35ppm cold and ~55ppm hot, but for me, it's wanting complete control over what goes into my body and the tap water filters and refrigerator filters don't cut it.
My fridge has a filter, but I don't bother with it since I do the distilling/filtering water.