I would do the shelves with a stopped dado. Cut the dado from the back and stop it 1-2" before the front edge. If the dado is, say, 1/4" deep, notch the front of the shelf that deep . This way the sides are continuous and you don't see the dado. I would do the same at the bottom using a rabbet. I think it is a toss up whether you cut the shelves into the vertical or the verticals into the shelves. Doing them the same way, stopped dado's, is going to require angled cuts either way. Have fun. Remember, it is not just kids furniture. It is something she will probably keep forever because her dad made it for her.