Which waters to use - distilled or deionized water?

Do not use deionized water in your boiler!
Use only distilled water in your small-scale steam boiler. Your engine will run on deionized water or even ordinary tap water. But there are problems with each of these which we should avoid.

Tap Waters:
Tap water contains minerals which will stay behind when you boil the water out of the boiler. When you run your steam engine, you are in essence distilling the water in the boiler. What comes out the regulator is pure water vapor, and the minerals are left behind in your boiler as scale. When you use distilled water in the boiler, there is nothing left when you're finished.

Scale reduces the boiler's ability to transfer heat to the water, and thus reduces the efficiency of your engine. Eventually, the lines may become so clogged with scale that you can't get any steam out of the boiler at all. Operators of larger engines can sometimes remove the scale physically by scraping or brushing. We have no such small scrapers and brushes, though. Scale can sometimes be removed by boiling vinegar or some other very weak acid in the boiler. This should not be considered a desirable alternative to using distilled water, however. Stick with distilled water and you won't have to worry about mineral scale.

Deionized water:
Deionized water contains no ions, which means it has had the chemically reactive molecules removed. If put into contact with metals, however, it will happily take on new ions, with disastrous results.