Because of the box design, the side guides can't be a straight but have a step. The guide i design is to be cut on CNC router from 3/4" plywood or MDF , but can be 3D printed as well. 

Since the middle wall is 1/2" the guides should be either attached with very short screws  either should be glued /nailed on place. Instead i decide instead one to have two holes 9 mm apart for each attachment point, that allows to use left on the one side and rights on the other with a 1" long screws. For the middle part a 1 1/4 " screws also can be used since the guide have bot holes anyway.  

For the side guides if 1 1/4" screw is used then the tip should be grinded, that's what i did. 

Assembling is simple, the only tricky part is to properly center the middle wall, i simply put marks on the bottom and back and use them as a guides.  Here is my assembly sequence : 

1 - add a chamfer to the side guides holes that will be used

2 - screw #6x 1 1/4" to the side guides, the screw tip protrude around 2 mm on the back side of the guide

3 - using screw tips center the guides to the wall, then pushing on the guide turn screw counterclockwise around 1 turn so it allow the guide to sit all the way top the wall and then screw it all the way down. 

4 - mounting side walls to the bottom, #6x 1 1/2" wood screws

5 - mounting back to the bottom/side wall assembly, 23 gauge micro pins

6- mounting middle wall, #6x 1 1/2" wood screws

7 - mounting the top, #6x 1 1/2" wood screws

8 - stain and clear coat - optional

9 - install the casters, #6x 3/4" wood screws - optional

I cut my back slightly larger and after i assemble the rack i trim it with a flush trim router bit. In addition to the fasteners i glued the walls, the top, th ebottom, and the back.