Showcase Lighting?

Will you have electric available?

Either way - knowing I've no real experience in this endeavor - my recommendation would be the small, thin (T5-size bulbs) fluorescent fixtures available at home improvement stores. They can be had in lengths of 12"-96", and can also be had as battery-operated units. Those won't be much more than 18", though.

They're small, light enough to be mounted inside the case with tape/velcro, and they don't burn out.

Don't forget, if possible, to also have a gooseneck table lamp available for closer viewing.