This is what you want:
http://www.amazon.com/Amazon-Kindle-...4196735&sr=1-1
It uses the battery in the Kindle for power, so no separate batteries to deal with. It is just bright enough, covers the screen, etc... I *LOVE* the lighted case for my Kindle Keyboard (older model).
[I'm making an assumption about which Kindle model you have based on the price that you gave.]