For dimensional stability, plywood is best. For shelving strength,
solid wood is better. For any given thickness of wood, plywood has
some fraction of it's layers with the grain oriented so it doesn't
add much strength.
For a roll cabinet, here's what I'd do:
Measure the width, thickness and depth of the shelf slots. Measure the
width of your cabinet, from outside-to-outside of the slots themselves.
Get someone with a thickness planer to plane down some oak or maple to
3/8-inch to 1/2-inch thickness. Your slots are probably 1/4" or 3/8"
thick. The length of your boards should be such that they are about
1/16" less than the width of your cabinet's slots. The stronger the
wood, the less thickness required.
Sand down the ends of the boards so they just fit nicely in the slots
without grabbing. Seen from the front, with the grain running
right-to-left, they'd look like this:
The important thing is that your grain is running from side-to-side in
your cabinet, not front-to-back.
You can edge-glue the boards together to make a solid panel that you
can slide in, or you could just lay out self-adhesive shelf paper and
put the boards down together tightly on that. The shelf paper would
mean no mismatched board seams for the rolls to catch on as you slide
them in, and might help reduce humidity issues. I personally would
glue the edges, clamp together lightly, wipe off the squeeze-out, and
then add the shelf paper.
Use the shelf paper on top _and_ bottom of each shelf board to reduce
issues with warping. You can probably leave the shelves loose in the
slots, but if you do want to attach them permanently, use a dot of glue
on the front edge of each slot only so they will expand in width in the
back, where things are hidden. Leave about 1/4-1/2" of space at the
back for expansion.