I know of one forum user who built a huge melamine rack held together with nothing but nails (no glue). But he used a brad nailer which tends to really pull the panels together. Also, when building a large structure with multiple joints any individual joint is more secure.
Now, with that said, I would not recommend using nails without glue.
For someone without a lot of tools I would recommend coarse thread drywall screws, making sure to pre-drill and countersink each screw. I would also use a melamine glue for any joint between an exposed particle board edge and melamine surface. Roo Glue is the most common melamine glue in the US.
Regular wood glue does not bond to the smooth melamine surface so do not use that.
There are other choices, including confirmat screws, dado cuts, pocket screws, bisquit joints, but I won't go into those with any detail unless you have access to the tools or don't mind buying additional tools.
For reference, my first choice would be confirmat screws with melamine glue. But that does require a special and expensive bit.
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Currently keeping a small collection of various Gonyosoma. Both G. janseni and G. oxycephala.