Reply to LED lighting options

I'm currently building a custom table for my gear . My design incorporates back lighting frosted plexiglass underneath the shelf to spell out the technics logo. Not having any experience with lighting, i was wondering what my best options were for a light source. I assumed LEDs were my best bet considering they can be pretty bright and come in just about any size/color i could want. The dimensions of the "box" are 42"X12"X10".

My specific questions are 1. Will the flexible LED ribbons produce enough light so that the transparent sections will be lit evenly( not bright in the center, dim on the edge)? Most of the ones i can find are only a single row.

2. If not what would be a better alternative?

3. Where is the best place to shop for this sort of thing?

The appearance of the lights dont matter since they will be hidden and if any mounting is necessary i can make brackets. Any advice is appreciated.