The best printing substrate would be a translucent polyester film, which is available for large-format inkjet printing in both matte and glossy surfaces. If you have a printer (whether an actual machine, or a service) that can handle prints of that dimension on paper, you're good to go (although it might take some fiddling to get a good colour profile for transmissive illumination). And dyes may work better than pigments for this application if there's a choice; you should get better detail and colour in the shadows with dyes. If you must use adhesive to mount, use it outside of the image area, otherwise the adhesive will telegraph through the image, since the substrate can't be thick enough to diffuse away all of the little differences.

The light box can be a relatively simple affair, using commonly available T8-type fluorescent daylight tubes with a good CRI in "home" fixtures (with a flicker-free high frequency ballast). You can also use a whole bunch of CFL bulbs, but that will be fussier to build and wire. A single sheet of translucent white acrylic of around 1/4" (5-6mm) thickness will even out any hot spots, provided that the box interior is reflective (painted matte white should do fine), and it will be cheaper and less fragile than opal glass. I would suggest simply holding the print against the acrylic diffuser with a sheet of clear acrylic in a "sandwich" frame rather than trying to use an adhesive; there will be a lot less opportunity to harm the image visually or physically.

Do note, though, that this will definitely be a display print with a limited lifetime rather than something with anything like archival longevity.