Della--I always use distilled or purified water to start my seeds until the have the first leaf. After that, I start using melted snow or a little rain water as Spring goes further along. When things look ready--about 10 weeks--I switch to my well water, which has a little Calcium in it (good). Throughout the Summer I save rain water when I can get it. But I don't store it for long. With my potting soil mix--that ends up in the seedling garden when I plant them out--I don't recycle that. Although I've read the Dutch industries recycle theirs up to five times when they use Coco (sp) fiber in the mix.
I don't recommend using city water. Here's another I wouldn't recommend to anyone: collecting rain water from the roof in one of those rain barrels. That might be OK for grass, but not flowers. A neighbor lady did that a couple years ago and she she ended up with so many weeds that she had to redo her whole garden. Apparently a roof serves as a great big 'seed collector'. And I surely don't want weeds in my seedling pots!