Steel yes, stainless probably not.
Basic engineering steel is strong, easy to weld and cheap. It's also heavy and rusts unless coated or painted.
Stainless Steel is less strong, can be brittle, is a real pain to weld, is hard, is very expensive and heavy. You use stainless where corrosion (or heat) is your issue and pick the grade (A2, A4 etc.) based on price versus corrosion requirements and strength/hardness.
Aluminium is relatively strong, can be cheap, can be brittle (eg when bent or vibrated), is very light and doesn't rust when untreated (it gets a protective oxide coat which is ugly but OK).
The traditional solution is a basic steel tube rack for it's strength, possibly with stainless nuts and bolts (avoids rusting together) and alumminuim boxes for the lightness of the big components. You thus combine the features you need. Other combinations risks undesirable features like a rack that will crack when struck and can't easily be welded as a fix.
If Aluminium boxes are an issue, I'd think plastic boxes on a powder coated steel rack, or the rack with soft bags might work better than big stainless parts.