I’ve not seen anyone ask this before, but in general plastics have a few overall characteristics:
Toxic - almost every plastic won’t be good for you. Be sure your ventilation is really good.
Dangerous for the machine - Anything with PVC (note, not “vinyl”, PVC… which is a very specific type of vinyl. You need to look carefully at the MSDS of plastics to find out if it’s actually PVC or even a vinyl with adhesive “vinyls”.) Be careful — if you’re wrong, cutting PVC creates acids that can damage your machine.
Flammable - Pretty obvious why this is a concern. Plastic tends to burn longer and hotter than papers and other thin materials.
Melty - This is often the case with thicker plastics more than anything, HDPEs, etc. Chances are a thin sheet of most plastics will let you move the laser quickly enough that this won’t be a big deal.
and Just Right - Acrylics vaporize more than burn or melt. It’s not to say that it can’t catch fire or that it’s not toxic to laser (I wouldn’t inhale those fumes if I could help it)… it’s just a really nice material to laser with.
Anyway, none of this is helping you directly, so let’s see if I can.
Dura-lar seems to be a bullseye. It’s polyurethane, which lases pretty well (don’t quote me, I’ve never used it but I’ve heard that it does.)
And maybe not adhesive-backed here:
Here’s more info: