1/4 is overkill. 1/8 or 3/16 is what I would consider. For the underside, 1/8 is plenty.
My reasoning is this only really matters if the cage is trying to pull out. The thinner 1/8 can deform but still hold. 1/4 just puts stress lines where it ends, more likely to tear the sheetmetal at that point.
Depending on where the legs line up, it is often on a factory body brace to start with. That make adding plates even more complicated.