Glue (reduces signs of consruction unless you use brass and cup screws as a feature). Screws if you need to flat pack them for transport and re-use.
You may get more responses on material if you share your design concept as size, construction and shape will be a factor.
By way of scaling i used 9mm plywood for creating a carry box and associated stuff for a bean to cup coffee machine. The joints were rebated or finger jointed and glued as the material woulf be too light to take screws. I also used pop rivets to attached clios and handles in order to achieve the asthestics of a flight case.