If you just want stiffer: a 1/4" bent-back lip top and bottom will make thin aluminum really stiff.
Just making a plate thicker is an expensive way to make it stiffer. Look at the floors in your house. If you have wood floors, they "could" just use very thick wood. But even for house spans and loads, that takes a LOT of wood. Instead they stand wood on edge as "joists" and lay boards across the joists: get much more stiffness with less wood.
1/8" is about as thick as many pots and switches will fit into.
Any metal supply house will sell you as much 1/8" or 3/16" metal plate as you want. The problem is that that don't like to sell as little as you want: they sell truckloads, or at least a 4 foot square plate, not single small pieces. A rack-face isn't enough metal-cost to cover their time to write the order. If you are lucky, they set their cutting fee high enough so they don't mind (can profit on) a little piece.
Steel is slightly stiffer than aluminum, but not a whole lot. When you consider the work needed to drill steel, aluminum is a much better plan. 1/8" steel is much cheaper in bulk than aluminum, but a real pain to cut and drill. In steel you always go thin, and bend lips to stiffen the edges. In aluminum you can drill 1/8" fairly easily, though if you need it STIFF you need to brace the middle.
