I think the hobbys shop plastic sheets, which are white and opaque, is styrene. There are some other transparent and colored that maya be PVC. So if using styrene a styrene glue would be best. A regular white glue might be best (or a carpenter's yellow glue) if you opt to use baltic plywood. The hobby shop can give you some good advise on which glue to use for the material you select.
Here is an example of the plastic sheet a well-supplied hobby shop should have: