Barrels won't do it. You should consider building a cistern or a small
pond. A one inch rainfall on 1000 square feet of area is 144,000 cubic
inches of water, which translates to more than 600 gallons. That means
you need a lot of barrels, and you have to plumb them together to make
use of the water. Building a pond and lining it with plastic sounds like
much less work to me, and is probably more attractive than a back yard
full of barrels.

True, but the positioning might prove more than a little difficult even on a
property as small as this one. Much of the water will end up being consumed
by various plant life, especially the trees, and a few additional plantings
should assist as well. I am considering putting in a water feature
alongside the house (which would be perfect for the runoff of a wall) so I
could likely direct some runoff into that as well. Hmmmmm....

One thing I wonder with gathering runoff like that -- sediment. Trying to
filter it out/clean it out might be a problem.

Thanks for the idea -- my spring/summer plans are beginning to expand.

James