Im not to sure about the rain water. I'm guessing it will be ok but maybe have it down spout into the filter media first.
I was thinking of getting this one
http://www.walmart.com/ip/My-Sunshine-8-Snap-Set-Pool/19336116
I see it at walmart for $18
Pool Material: PVC
Specifications:
Dimensions: 8' x 18"
Holds 552 gallons of water
I have a old little pond filter around some where. A pool filter works for a natural pond?