will it sag

I think you’ll be alright. Looking at a quick picture of the shelves in question it looks like the shelves are about 36” wide on bottom, but the dividers on the upper shelves will actually support them in the middle, so at 18” I think you’ll be fine.

What veneered ply can you source? Especially with a dark stain birch ply and cherry blend together easily, and if you want a lighter tone, you could just build the whole thing from birch and stain it a medium tone.

Hard to say. Mdf has its purposes, but I wouldn’t use it for shelving. I would tend to use an alternative wood rather that mdf if the cherry is unavailable simply because shelving tends to hold stuff that will eventually warp the mdf. Just my 2 cents worth…

-- Power tools put us ahead of the monkeys

I dont know the width of the mdf, nor if its face framed or has a solid front edge (helps) but if its over 32” wide (even that, it’s “iffy”) it will sag

-- "Good artists borrow, great artists steal”…..Picasso

That bookcase calls for a face frame. You can double up the mdf and it will never sag.

-- He who fights with monsters might take care lest he thereby become a monster. And if you gaze for long into an abyss, the abyss gazes also into you.

If forced to go with fiber board, you would be better served with HDF (high density fiberboard) as opposed to MDF (medium density fiberboard). Engineered wood flooring may also be an option.

Go

-- Go http://ncwoodworker.net/pp/showgallery.php?cat=500&ppuser=730

You could get a rough idea of the deflection by running the sagulator for different materials:
http://www.woodbin.com/calcs/sagulator.htm