If you have distilled or the reverse-osmosis water dispensed from machines in the supermarket then you may as well use it. Using deionized water is likely overkill.
Tap water is probably fine, but my beef with it is that its composition can change with the seasons and I don't know if stuff like chloramine (a commonly used water supply disinfectant which doesn't dissipate like chlorine does) can react with the soup of organic molecules being extracted--tap water may affect repeatability, or in the worst case generate chlorinated compounds.
Two things to keep in mind:
1) It is all lies.
2) There is no privacy on the Internet.