I would not be too keen on using rain water these days given the complex contaminants in the air . The virue of spring water is that (unless some sod buries a horse next to it) the water has been (often) filtered nicely by the ground layers . They are however liable to surface water contamination from livestock and surface agri chemicals . All in all , unless you are damn sure of the consistency of your alternative supply , tap water is your best bet .
Until coming to this forum I had thought that chlorines gassed off when tap water was left to stand . It appears that in recent years water companies have taken to using chloramines that smell less and hence do not gas off . So the use of sulphites as a neutralising agent is more important than ever . Campden tabs give you the best measured dose of sulphites and will do no harm to your brew as THEY will gas off nicely and take care of any nasties as they do so . In fact a 10% spray bottle of sodium met/campden is a handy thing to have around to make sure of chlorine neutralising on cleaned kit and things that you handle .