I finally got out and bought my plant brackets. They cost way too much. I wanted little $5 brackets, but since they had to be at least 15" the only ones that fit the bill were very heavy duty brackets. The light is incredibly lightweight and really doesn't need all that metal.
When I put them up I brought out my handy dandy stud finder, only to find that the battery died. When I took it out the whole plastic/metal part that connects it to the rest broke off. So I tried doing it the old fashioned way, rapping my knuckles on the wall, to no avail. I have thick real plaster walls and the window and ceiling are very close together. So I just put the brackets in the plaster. As I said the light is very lightweight and the plaster is thick. I think they will hold just fine.
The light is plugged into a timer and that will be plugged into the wall. They hang from chain so they can be adjusted. The whole setup is ready to go when I need to start seed in exactly one week. In the bright midday sun the blue LED light seems pretty weak. I was worried about seeing my plants, but during the daylight I should have no problems. Now I'm just crossing my fingers that the LEDs can make stocky seedlings. I'll let you all know in a month or two.
March Update: go here to see how the LEDs did. See the last paragraph on the page.