First thing first, I have had inconsistent luck using Home Depot or Lowes to cut sheet goods accurately on their panel saws. I believe they have a policy about not allowing stop blocks clamped to the saw which is the best way to insure accuracy. Even then you assume a consistent straight/square edge to work off of so a stop block does not always work.
Racks recquire tight tolerances so I'd at least look into having a local cabinet shop cut your material for you. In the past I have found that they are thankful to have simple cuts that keep their entry level employees busy.
If you do have Home Depot cut it for you, at least shoot for the largest sized panels you can get out of the number of sheets you need. By having them oversized you have the option of getting them square and consistenly sized later.
Also, regarding the use of plywood, understand that plywood has gone down in quality in recent years and is often full of voids and of inconsistent thickness. Both can cause problems with racks.
Baltic Birch plywood (the real stuff from Finland and Russia that comes in 5x5 sheets) is much better and the odd size often makes it better for larger racks with deeper shelves like yours.
Unfortunately a warm winter last year means they were not able to cross some of the rivers to get to the timber so the prices have gone up on real baltic birch.
At any rate, consider melamine. It is flat and the thickness is consistent. It is also super cheap, especially when considering there is limited finishing involved, if any. And some of the 6' long melamine shelves actually end up being cheaper than full sheets once you factor in waste. You'll have to figure that out yourself.
Okay, onto the measurements...
Each rack will hold three tubs, meaning four shelves at 0.75" each, or 3.0" in height due to shelves. Two boxes at 6" tall and one at 9" tall means a height of at least 24".
I would recommend keeping all of the shelves the same width so you can space out each level. At the very least only have the top or bottom resting on the sides rather than between the sides. To have both the top and bottom resting on the sides means you'll have to cut your sides perfectly. If I were to do that the only way I would try it is to have the sides cut longer than needed to each space could be made oversized and shimmed to fit the tubs.
Or have the tubs run on rails so the spacing does not matter.
So I would do it this way:
Four "sides" at 25" x 36"
Eight shelves at 18" x 36"
I would not include a full back for racks this small. Instead I would just use some scrap to cut a partial back piece and fill in the rest with Reflectix insulation. You just need enough material to stop the boxes from sliding and to help hold the carcass square.
I think your design is a bit complex and asking for trouble due to the lack of accuracy achievied with a panel saw. I would simplify it as much as possible, if possible.
The only reason I'd modify the suggestions above is if it just did not work with the stock sheet or shelf sizes you found locally. I do not like storing scrap lumber so I'm willing to modify designs in order to avoid buying an extra full sheet for one shelf, for example.
-----
Currently keeping a small collection of various Gonyosoma. Both G. janseni and G. oxycephala.
