It might help to see a wider shot, so people can tell what kind of lighting might go with the rest of your room, or what level of lighting might be needed. The scale of that stool is quite small. I would think of a floor lamp there, just from the photo, but without seeing more of the room/corner, it's hard to say.

it's a tight corner, so keep it light. I would go for a chair with open framework and straight lines (referring to the book shelf) and a side table that goes along with it (entu side table in my example).
I kept your light but for serious reading you might want something more like a desk light. I'm not really satisfied with the chair (lines need to be more straight and little bit thicker) but here's a quick mockup:

Are you looking for a light that illuminates the bookshelves from top to bottom, bright enough to read the titles on the brown books on the bottom shelf? Or are you looking for a reading light for a table?

Ikea has a selection of bookcase and cabinet lighting that you might want to take a look at. You could clip a couple of their lights on the top shelf of your bookcase unit. In the meantime, maybe your current lamp is short enough for you to move some of the books and place in on one of the shelves.

Alternatively, a floor lamp, with or without a chair.

How about Ikea Holmo floor lamp. (not my picture just found on google images to show example)