Have you considered a bonsai tree? There are several tropical trees that will grow nicely indoors under a grow lamp or simply near a window.
Based on your "woody stem" requirement, I would recommend something like a Chinese Elm or a Ficus trees. Most Ficus Bonsai Trees will lose their leaves when they are moved to a different growing conditions (indoors, under a light), but that will also give you a chance to see the trees branch structure.
To answer your light question. Ask your local home improvement store guy for a plant bulb (Fluorescent bulb). But remember, most plants, including the Ficus needs some darkness. You also want to purchase an inexpensive timer for your light. Good luck
You should be able to find several sources online for growing a bonsai tree indoors, including http://www.BonsaiOutlet.com.