Thickness of Acrylic for shelves with 39" span
Acrylic is not very resistant to bending. It is about 20 times weaker than tempered glass. 

0.75 acrylic would be marginal. It would have enough bow to be visible to a sharp eye. And it scratches easily, as Ecnerwal mentioned.

I would recommend 3/8" tempered glass. Definitely tempered, much stronger and safer than plain glass.

And be aware that you cannot cut or drill tempered glass, it will shatter. Get the size right the first time.