The best way to stick it, is to ensure you use a low grade sandpaper, around 300 or 400 to rough up the back surface of the styrene, and then use the same sandpaper to rough the surface of the wood, and use Araldite, or any 2 part epoxy glue.
Superglue becomes brittle and styrene cement only allows for the stryene to stick to other styrene effectively.
If it's a long lasting strong finish you are looking for I would use Araldite.
Good luck.