I see a lot of nonsense poster on various forums about water. Essentially there are two problems to worry about.
1) Boiler scale
2) Electrochemical replacement
Boiler scale covers the deposition of any dissolved solids into the boiler and water lines. This reduces the efficiency of the boiler by reducing the heat transfer rate across the deposit. Deposits can also build up to the point where they narrow or block tubing or a piece may flake off and be carried with the flow and lodge somewhere possibly blocking the flow. Boiler scale may be soluble in insoluble. Soluble deposits may be removed by flushing the affected area with hot water. In soluble deposits are most commonly calcium carbonate which is dissolvable using weak acid. Do not be tempted to up the acid strength if the deposit does not dissolve as gypsum (calcium sulfate) or alums will not readily dissolve in acids. Soluble boiler scale happens any time the water contains a lot of disolved solids of any PH. Insoluable boiler scale mostly happens in weakly alkiline solutions.
Electrochemical repacement is where a reactive metal in the boiler metal is pulled into solution to release a less reactive metal from in the solution. Copper, Iron, and Hydrogen present as ions in the water will all preferentially replace Zinc. This is usually a problem with brass boilers but may also attack silver solders depening on the exact alloy composition of he solder. Often the precipitated metal will also form insoluable boiler scale. The general problem here is the weakening of joints and the boiler structure. The Australian miniature boiler codes prohibit boilers made from certain alloys and also certain compositions of silver solder that are known to be vunerable to this form of corrosion. This usually occers in water that is either stongly alkiline or mildly to strongly acidic.
Just because the water has neutral PH does not mean it is safe. You have to also know the total dissolved solids and Ionic concentratons.
Steam distilled water, dehumidifier / dryer water and refrigerator ice are the most pure sources of water but be aware of what the wayer may be in contact with.
De-ionised water is created by passing the water through two columns filled with ion replacement resins. One that traps all the positive ions and repaclaces them with hydrogen and another that similarly replaces all the negative ions with hydroxide. Negative hydroxide plus positive hydrogen equals water. Bingo pure. Unfortunately the manufacturers can run the colums too long or improperly regenerate the resins and substantial contamination of the product can result.
Rain water is very environmentally dependent. It can be very pure or it can be quite acid or salty depending on how close to the sea you are and wether you have downwind pollution. It usually contains substantial dissolved gasses which can be a problem in theit own right. The worst rainwater can be far worse than the worst tap water or de-ionised water.
Tap water always contains substantial dissolved gasses most especially chlorine which can react with copper in a way that very little else can. Tap water is usually treated to be neutral or slightly alkiline which makes it better that rain water near a pollution source. Tap water may contain substantial dissolved salts. Water from the hot tap may also contain substantial dissolved copper and zinc.
Is any of this a problem ... maybe not. If you have a properly constructed boiler made with good silver solder and you never have to descale your kettle then tap water may be perfectly acceptable. Just boil it first fro a minute or so to drive off the dissolved gasses.
If you have a heritage boiler of one of unknown provenence or you used cheap silver solder or you regulaly have to descale your kettle then use a purified water.
If you are paranoid go to a yachting supply store and get a small zinc sacrificial anode. Cut off a small piece and drop it in your water storage container. Anything that will attack your boiler will hopefully be used up attacking the zinc metal.
Getting an ion concentration meter may also be good if you can afford it. Test stuff and report back here!