If you can find 3/8 or 1/2 clear acrylic, that would be best. Would not use 1/8 inch, too weak unless braced allot which kind of defeats the purpose of a "shadow free" work area.
1/4 acrylic will work but then again, I would brace it pretty good. I worked at a place where we use acrylic to cut out signs etc. and the thicker you can get it the better. Also, be careful with the sheet, it may seem stable, but it does break, chip, easy ( 1/8 or 1/4 ) if handled roughly, until set in place.
Nice idea and interested in seeing the finished table.
kgstakes's post in Light table question was marked as the answer