The item number for the cubes is DL46401, but you may want to check it with a representative before you order. I bought them to make barriers instead of cages. They are 12 x 12 inch grids. The name is 'Great Cubes' Interlocking Grid Storage System. Anyway, about supporting the shelves.
Dimensional lumber comes in a wide variety of sizes.
The length of the piece is independent of the measurements given for the size of the sides. The wood is always somewhat smaller than the numbers. I usually leave about one inch sticking out of one side, and at the other side, where about 5 inches are sticking out, I cut it off to only 1 inch, cutting off a 4-in.