How To
Thanks everyone. It turned out better than I expected. To Bekers71, TandJ, and anyone else interested, here is how I built the rack:
Materials (lumber from Lowe's and sterilites from target)
2 2x4x12's
1 sheet of 3/4" thick medium density fiberboard measuring 97"x49"
box of 1 5/8" screws
8 32qt sterilites (#1756)
Shelves (8 measuring 16.3"x24.5", and 1 measuring 16.3"x26.5"
First cut the fiberboard longways into 3 identical pieces: 49/3 = 16.3"
This is perfect because the containers are 16" deep. The length of each of the 8 shelves needs to be 24.5", so cut these from the 3 long pieces of fiberboard. You can only get 3 shelves out of each one. The 9th piece has to be longer so it can be screwed into the top of the rack (I wouldn't cut this piece until the very end just to be sure).
Legs:
Cut 2 legs out of each 12' 2x4 measuring 60 7/8". Now for each leg you will need to cut 8 dadoes that are 3/4" to hold the shelves. Set your saw so that it will only cut 1/2" into the 2x4s. Start from what will be the top of a leg and measure down 6 7/16" (this is going to be the vertical space for each sterilite). Draw a line here and another line 3/4" down from the first line. Now clear out this 3/4" space (dado) with the saw. Then measure 6 7/16" down from your first dado, make a line, and another 3/4" inch down. Repeat this process until you have cut 8 dadoes. Then repeat the whole leg process for the other 3 legs (it took me 30 min for each leg).
As you cut each dado, make sure that a shelf will fit into it. After cutting all the legs, I laid two side by side on the floor, dadoes up, and fit the 8 shelves into them. A hammer helps for the snug fit. Then I laid the other two legs on the shelves and worked them into place. After hammering boards here and there to where it looked best I predrilled my screw holes (the fiberboard will split if you don't). I put two screws into each leg/shelf connection. Then turned the unit over to screw in the legs that were touching the floor. Finally I stood the unit up, measured my 9th fiberboard piece to fit on top, cut it, and screwed it into the top of the 2x4 legs.
The bottom of each leg should measure about 3 3/8" below the first shelf so that you can screw in a cut 2x4 for extra leg support but I found the rack was already VERY sturdy.
If anyone finds this confusing, I'd be happy to clear it up.