Some notes on dovetail type construction:
-Dovetail is weaker than half dove tail.
-Dovetail joints in plywood have to be relatively loose, since the end grain doesn't slide well. Too sloppy for my liking for this application.
-Make sure you clamp your material flat before making any router passes or your joints will be off as much as the non-flatness of the wood.
-Seal the wood before doing anything, it will keep movement to a minimum and make dealing with squeeze out easier.
-Use one router bit ONLY for all dovetail cuts, and make sure it doesn't make a glue line cut at the bottom of the groove. Two bits may not be exact matches.
When using boards, I only use tapered half dove tails. Blind if I'm feeling lazy about the fit, exposed if I'm going to show them off. Full dovetails have nothing but downsides in comparison.
I never use any kind of dovetail when I'm using plywood, too sloppy of a joint. Only butt (paint grade work) or dado joints (finish grade work).
If I were doing this in plywood with edge banding, I'd put the edge banding on first, sand, seal, cut blind dados. cut shelves, and use a template and router so that I can have the shelf fit in the dados and get the edge band at the front compressed for a tight front fit during assembly.
No matter what you choose, holding tolerances and avoiding cumulative errors is always a good thing. Some methods are more forgiving than others, and joint surface roughness is more important in some than others.