I'd use 3/4" for the sides and shelves, 1/2" for the back and doors. Do
no tuse particleboard of MDF as it will be prone to sag.
....
Polyurethane.

Thanks for the good advices. I definitely will not use particleboards.
I got too many sagging book shelfs that were made from particleboards
that I bought when I was in college.

Jay Chan