I've made several. I posted one to the library:
I'm not sure about the best program to use, but there are a few free options online. I ended up using this one the most.
Layer thickness is going to define the "resolution" of the print. I made mine on both stereolithography (.003" layers), and a Polyjet printer (.0006" layers). The Polyjet is better, but from a viewing distance of of 2-3 or more the difference is really not that noticeable.
Another factor you pointed out is material. It needs to be translucent. An opaque material is not going to allow enough light to pass. Transparent materials don't diffuse the light. It can take 1-2 sample prints just to get a good idea of what thickness range is good for a given material. From the Polyjet I use Vero White.
UV stability must be considered. Vero White is amazing in sunlight. I've had the above skull in my window for years and there is no trace of it yellowing. The stereolithography materials would be yellow/orange by now.
Thermal properties are another factor. Vero White is pretty bad with heat resistance. Warm it up a little and it will sag. For best results I'd place the print in a frame to support it.
It adds some complexity, but you could also print or machine a pattern for the lithopane, create a simple open faced mold, then cast duplicates in a suitable material.
These make great gifts. I'd "borrow" photos off of peoples desks in the office, then make a lithopane for Christmas time.