Even the rain/dew off a building roof would be fine for UTILITY water...
Downspout drains are fine for collecting drinking water if you let the bird poop, leaves, bugs, ect, clear out before you start collecting.
Plastic collection containers are most effected by the suns UV rays, so if you keep them out of the direct sun light, or use UV protection for plastic, it will probably work fine for long term use.
There are very large plastic containers made for collection of liquids, particularly water, that can be purchased at about any farm store.
Everything from 5 gallon buckets, to barrel sizes, to over 1,000 gallons.
Long term storage of any water will require treatment for that water to keep it from growing bacteria.
If you intend long term storage, make sure your storage container is rated for the treatment chemicals you intend to use.