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.