What should be the thickness of a glass table top
1/4" tempered glass should be fine. It's considerably stronger than the same thickness of normal glass, and also much safer in the event that you do manage to break it.

LED (or any other light source) into a glass sheet is normally injected at the edges (the LEDs being built into the table frame) - but it may not be all that exciting on a clear glass sheet (the ones you linked to were heavily textured - it needs to at least be frosted on one side for much light to get out.)