Hey Byron and welcome to the forum.

I have this particular orchid, and I grow it on an east facing window in a medium bark chip mix. I think it should be pretty happy with your florescent lights. I water a couple of times a week as it seems to like it a bit more wet than most of my oncidium hybrids. If you're going to fertilize weekly on this one, I would fertilize with something around a 30-10-10 fertilizer at about 1/10 recommended strength.

Also, feel free to check out the American Orchid Society's PDF care sheet HERE.