Typically, your choices fall between a fabric and paper type.
Fabric lampshades have the advantage of being more durable compared to paper types. They also come in different forms from cotton to silk. The downside with fabric is it's costlier and requires a bit more of maintenance.
Paper lampshade is the cheaper option. It also comes in varying form of thickness from the thin ones to the width of cardboard. Paper is also better does a better job of blocking or directing light. On the downside, the paper is not as durable compared to fabric.
The key to finding the right vintage hula girl lamp that works well with your situation is knowing how to filter your options effectively. With the key points mentioned above, you should be able to narrow down your choices to a manageable list.