Plywood shelves: do i need to cover the cross-cut before painting?
if your just painting it why not go with flat stock mdf? its cheaper and easier to work with. you can simply sand the edge or put a small routed edge on it then paint.
regarding the actual paint process, if there any tight spaces on it, consider pre painting all the components with one coat of primer and one coat of the finish color before assembling, it will make it that much easier to get into the corners when you do the final coat