What is the best way to fix a large rectangular shaped glass table top?
Call up a glass shop and order a hunk of tempered glass the right size. You can't change the size or shape after it's ordered (tempered glass can't be cut after tempering), so get the size exactly right.

The one you had was not tempered, or you'd have a few thousand more pieces - which is a lot safer than one that breaks into fewer large sharp pieces.

Tempered glass is much stronger than normal glass of the same thickness, so one the same thickness should hold up to your use, but you could always go to 3/4" or 1" thick tempered for even more durability while staying with glass. 

Or go with a few thousand years of experience and choose wood ;-)