I think the hobbys shop plastic, whcih is white and opaque, is styrene. So 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.
The adhesive that's used for this plastic sheet Brian is a solvent cement that "welds" it together , like the adhesive that plumbers use to join plastic cold water pipes, they sell it in model shops.