Go with the distilled water. As Terry said re: mineral free, etc. Also tap water has crap added that could react w/all the different surfaces it has to come in contact with.
Re: BMW Coolant vs Aftermarket - I'm an avid "true blue" fan but if you stay up with the bi-annual coolant flushes and stick w/major brands - I don't think you'll have any issues. Without going into a chemical lesson, the BMW coolant has a "smaller expansion" factor when hot vs the aftermarket brands. (amongst other minor additive issues)