Oh ok cool, Akro Mills 64 Drawer and the Akro Mills 24 Drawer
Small pieces: Akro mills 64 drawer storage drawers. Sort by shape and consider grouping similar parts.
Medium pieces: Akro Mills 24 drawer storage drawers.
Large pieces: Just get 2-gallon buckets with lids from your local hardware store.
Labeling: Take photos of each part on a white background. Cutout the part from each photo and tape or glue it on the front of each drawer.
I think you might be looking for drawers like these?:Option 1Option 2Option 3Option 4They're all just variations of each other in different sizes & numbers of drawers, all plastic, and around $30 and under. The dimensions are slightly off, but you might be able to find ones that are a little closer is space is a constraint.
If these don't work, you might have luck searching for 'hardware and craft storage drawers', which gave me these on Amazon :)
Those are down to $30...