I do use distilled water for mixing, as well as drinking. I like distilling because it takes out all the impurities, and then I can add stuff back in to structure it.
As far as for mixing with Miracle-Mineral-Supplement , I think any relatively pure water will do ... it is not as significant as the liters of water you should be drinking. Usually the filters on a fridge are not the greatest, but certainly better than drinking tap water.
Try to get to a point where you provide yourself with the purest water you can for drinking, but don't worry to overmuch about it to start with. Use the filtered water from your fridge just to get going.
I do heartily recommend adding something to the water and Miracle-Mineral-Supplement to help with taste ... I usually add some green powder mix or something. Another way to do it is to blend up something, say a carrot along with some water, and make a small carrot smoothie and put the Miracle-Mineral-Supplement in there.