Edge-lit light boxes
I don't think it matters too much whether it is fluorescent tubes or led. I know LED is slightly more expensive but with a lower running cost and less heat.
In terms of flourescent tubes, the backlit light boxes are generally deeper, so you probably want edge-lit light boxes. All of the LED ones I have seen are also edge-lit.
CCFL (Cold Cathode Fluorescent Lamps) produces far less heat than T5 fluorescent illumination and lasts 2-3 times longer than a T5 fluorescent tube as well.
One other option is to use Electroluminescent Technology, which is paper thin and flexible:
www.w-co.co.uk