Here is an example of fastening parts in a perpendicular join with a common acrylic screw. Also shows joining layers together with a spring pin. You should be able to assemble any structure you need with these two techniques. Layers create a countersink for the screw head.
I’ve worked up a dozen or so other techniques for joining parts together (custom 3D printed clips, etc) but this is lowest cost and the strongest technique out of the set. No glue required.
Example source of fasteners: