video Rain water collection / filtration / storage system howto
This video shows a 300 gallon system to store water that is scalable using 55 gallon plastic drums and inexpensive components. Should be enough information for you to take from it what you need and make your own version. Hope it is helpful!
I'd think that if you used blue/opaque barrels instead of the white that would help, or perhaps put either a roof over the whole affair or put a tarp over all of it, that would help.
Personally, as long as the algae doesn't clog the lines, I wouldn't care since it's a great source of plant nutrient...
I think your setup is one of the most efficient ($) at hooking barrels together. This one is similarly efficient, but gives 6 foot of water pressure when full:
http://www.rainharvester.blogspot.com