I use these aluminum extrusions a lot at work and some at home. The challenge I've found for spec'ing panels that fit in the channels is getting a material that is a true .250" thickness. Everything after that is a balance of your budget or how robust you want it to be. I'm making the assumption you're talking about the 10 series extrusion (1").
The birch plywood is only .203" thick which leaves an almost .050" gap between the panel and extrusion. It's cheap (at only ~$20 for a 4'x8' sheet) and would be a good option for test fitting before cutting more expensive material.
Coroplast, ABS, HDPE, acrylic, laminate flooring, laminated aluminum panels, etc. all are around .200"-.236" even though they seem to be advertised as "1/4".
Note: .236" = 6 mm and seems to be the most common
Another option is to find a 3/16" material and run a panel gasket around the border of the panel. This lets you run a thinner (ie. lighter/cheaper) panel but has the extra cost of the gasket. It may cut down on rattles for cabinets built in a van.
My original plan was to use ABS plastic but the thickness has me hesitating. I use a material at work called Garolite but it's expensive and heavy, 2 things I don't want for my home project. For now I'm using cardboard as my prototype panels to make sure everything fits.
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