I have used all of the above except for HDPP in a herp application of some sort.
I would prefer 1/2" expanded PVC for racks housing small/medium colubrids and/or "live-bearing" species.
For racks housing species that are not quite as good escape artists 1/4" would be acceptable but then there are jointery problems (unless you have a thermal welder).
For cages I would use 1/4" expanded PVC assuming the listed weights I have found are correct. What I mean by that is that the listed weight for 1/2" (not 1/4"
PVCX is anywhere from 38.5 lbs. to 70 lbs.
If the weight is indeed 70 lbs. I'd rather just use standard core laminated plywood which weighs about the same. If I really wanted a plastic cage I would learn to work with the 1/4" material. For me the biggest advantage of a plastic cage would be weight savings so I could not see building a plastic cage that weighed the same as a plywood cage.
If I were able to find 1/2" PVCX at 38.5 lbs. I might spend the extra money. The 1/2" is much easier to join (screws, rivets, dados, rabetts can all be used) than the 1/4" and will have better insulative values.
I suspect that 1/2" PVCX really does vary that much in weight. One well known plastic rack builder has weighed the 1/2" product he uses and it is just about 70 lbs. But I also know two other people who have found 1/2" PVCX products that are listed at 38.5 lbs. So unless the weights they found were for 4'x4' sheets I'm inclined to believe different densities are available.
However, PVCX is probably not suitable for lizard species that scratch a lot.
I have tried to cut ABS with different tools and always got a very rough edge. As such I think it would be a lot of work to get an appropriate edge for solvent welding. The 1/4" material I used also seemed more flimsy than the 1/4" PVCX I had.
However, ABS had a very smooth surface and seemed extremely strong. Perhaps the ideal material for plastic forming.
HDPE is freaky strong but I had trouble finding sources with straight and true sheets. All were warped to some degree. It's also very heavy. PVCX, on the other hand, has always been very straight.
Melamine is a great material for building racks (provided they do not need to be moved or shipped). Use 1/2" plywood for the sides to save weight.
For cages melamine is much too heavy and sensitive to moisture. I much prefer an epoxy sealed plywood.
Back to plastic, if you don't want to buy a thermal welder I recommend solvent welding 1/4" PVCX. Edge to surface bonds (aka a typical butt joint) are very weak with this material so I recommend reinforcing them wiht 1"x1" PVC corner angle. This will essentially make a surface to surface bond which is extremely strong.
To summarize, first figure out exactly why you would want to use a plastic. If it's only for ease of cleaning there are ways to mimik that with different interior coatings (anything from plastic sheets to contact paper to epoxy) on wood cages. If it's weight savings you might find yourself disapointed if you use anything other than 1/4" PVCX.
But there are other reasons/advantages to use plastic.
Good luck and let us know what you use.