well, deionized, the way that page describes it, and the way i interpret that, is the worst to use for anything except certain laboratory experiments that absolutely require it and if you needed deionized, i would think that you would absolutely be aware of that fact because you would be a chem student or a chem professional conducting said experiments.
now, other than that, i don't think it matters a whole damn bunch at all as long as you do to it whatever is needed to make it right for your purposes. If you have well or tap over 200ppm or even more, do something to filter it (RO) or buy store bought. if you have tap or well under 100, awesome, perfect, use all you want. i have even found webpages that contradict the need to 'dechlorinate' any water you use.
distilled water can be harder to work with sometimes because in order to conduct electricity, or in other words, be able to measure pH or EC or TDS it has to have something in it. distilled is so neutral to begin with it cannot be accurately measured. it is fine to work with after you start adding stuff, just like any kind of store bought bottled water that ain't really weird or special. just store bought drinking water is awesome. tap water is awesome, like i said, as long as it isn't crazy with some chemicals you don't want in it or it's just way over the accepted starting point ppms for the nutes you are using.
test your tap for ppms. or whatever water you want to use. as long as it is close to 100 or lower, AWESOME, go for it. i used to use distilled only, but the reading fluctuated too much even after mixing in everything i was going to. i also used to drink it. then i did some research on it and found it that it ain't exactly as healthy as it is tasty. living organisms need natural water, like what you would find in nature, spring water. not distilled, not processed (city, but city will do in a pinch), but just water. we adapt to our environment. Darwin was right and it applies to everything. everything is relative. (Einstein was right, too).