Hi,
You would be surprised at how much of an area of acrylic you can light up this way, but its also dependant on the LED's used. The nice thing is you can have a few different sets of LED's lighting it so you could set up coloured "mood" lighting.

The light you will get will be diffused quite a bit and while the acrylic will shine fairly bright, it won't light the Tear up very efficient. I think it would be cool, but would also include normal lights for reading etc.
You can do almost any design that looks good black and white, its very much like etched glass.
Stick with an acrylic, for example plexiglass, lucite etc., its cheap and durable. Either sanding or routing works,, another option is to have a shop that has a cnc engraver engrave the pattern you want in. The area engraved will be the area lit up.
Cheers
Regan