I always have lots of scrap wood sitting around and love to be able to put it to good use.
I picked some 1/2" birch Use what you have. Just modify your dimensions.
1/2 birch plywood ( I love birch for a lot of projects. It paints or stains nicely)
Saw of choice ( I used a table saw to rip the pieces but most anything will work)
1/4 inch plywood for back
The design is pretty straight forward. I ripped the 1/2" birch down to 4 1/4" wide strips. I cut (5) 18 3/4" long pieces for the top, bottom and shelves and (2) pieces at 15 1/4" for the two sides. I spaced the shelves approx. 2" apart. Apply glue to the shelf ends and nail on the side pieces .
Cut a 19 1/2" by 15 1/4" piece from some scrap 1/4" ply for the back. Check your box for square by measuring diagonal corner to corner. Run a bead of glue around the perimeter and nail your backing on.
Load up your handy paint shelf. I like storing it backwards to see the colors better.
My kids just attacked the paint today to paint little boats they made for floating in the rain gutter after a much needed storm. I hope you find this as handy we do.