I started with a coat of primer, followed by two coats of a solid dark green, and finished up with experiment I am about to share with you.
I will say that I did not completely solve the mystery of how to best paint a very smooth plastic barrel. I am wondering if I should have roughed up the surface with some sand paper before I even started. The paint has been chipped in a couple of places. A chunk is peeled right back to the original smooth plastic.
Since the rain barrel will live in my garden I wanted it to look like it belonged. I suppose the other tactic would have been to transform it into an eye-catching piece of artwork. I did consider this... I mulled over coating it in broken plates and mirrors. At any rate, I finally settled on the more "natural" look by choosing two rather tame shades of green.
The result looks rather abstract and textural but I am happy with it. I got so excited about the fern and the reverse side of the hosta leaf (where the veins are thicker and pick up paint better) that I printed some on paper. I might just scan them and make some notecards or stationery with them.