Water chemistry is maybe one of the most complex topics in brewing besides yeast. To keep this not too technical I'll just summarize some major points that should help.
Using distilled or RO water solely for AG brewing is actually detrimental to your beer. Many think spring water is better but in actuality it may be just as bad for the opposite reason depending on the source. That reason is that minerals in the water are needed for proper conversion efficiency, taste and yeast health. Distilled water has 0 minerals so you are really not getting all you can out of your beer. On the other hand some spring water may be too high in certain minerals (Mg, Ca, etc.) so certain off flavors may show up in the brew (harsh bitterness for example). If you want to use spring water make sure you are able to get a water analysis sheet from the company you use and verify it is a good profile for brewing.
I recommend downloading John Palmers spreadsheet from howtobrew.com to help you determine a good water profile and how one should change it. I also HIGHLY recommend downloading the 4 part Brewstrong podcast on water chemistry to gain a basic knowledge of what waters role in brewing is.
Since you are already willing to use distilled water for brewing, a good way to make your water perfect is to build your own profile from distilled using various salts and minerals, easily available from homebrew stores, so you can have a customizable profile perfect for the style you are brewing. You can do this by using the water spreadsheet from John Palmer.