Is it better to stain before or after assembly?
Before if you can.  It will be far easier to stain/paint while disassembled, plus you can lay the pieces flat to ensure an even application.  If parts happen to shift a bit during use, there will be no noticeable sections that are not stained/painted.

You should try staining a scrap piece of your plywood first to see how it stains, sometimes the results of stained plywood are not great.  Painting is sometimes a better option.