Watch out, Jim, most storage shelving is MDF that's been melamine or otherwise coated.
Everything else being equal, MDF has very little resistance to sagging...ie weight bearing ability is pretty poor. Plywood is much better and solid lumber the stiffest.
Again, 5/8" plywood is sort of OK but 3/4" is far superior for long term weight bearing. Each shelf, assuming they're adjustable, needs a vertical front and back solid wood facing...3/4" x 1 1/4" would be my choice...glued on (flush with the top surface of the plywood).
Assuming it's around 2' x 2' you can stand on that without deflecting it!