Demineralised water is more pure than rainwater is more pure than tapwater.
If you live in an urban environment, it's closer to tapwater from absorbing carbon dioxide (turns it to weak carbonic acid) and etc from pollution in the air.
If you live in a rural place, it's much closer to demineralised water.
Either way, wait out the first 10 minutes or so of rain to 'wash out' the air, and then collect water after that. It's the cleanest you're going to get.