The only good advice I can give is trila and error. Thick styrene (.060) gets gloppy and burns with the right speed pass to cut through. I got .040 to cut, but also got a bevel on it (what's up with that)! I got thinner plastic to cut clean (.020) for skinning frames (made big things lighter). The thin can be cut without burning or marring. You just need to adjust the speed and power settings to get it work.
The acrylic (because of its properties) should cut clean through. I cut 1/4" acrylic with paper covered sheets and made trophies or plaques. Then there's adding LED light to the edges for affect...
Try the moistened paper tape. I also found sometimes on straight plastic (regardles of thickness) that a second/third pass could cause flameups/fire. But paper lined could take the power on a single slow/hot pass with minimum flame. The paper also protects the plastic from marring and you only have to peel the tape up afterwards.
The attached photo object was a rectangle cut from 3/16" acrylic (rastor etching and vector cutting used). Clean, glossy edges. You could make some REALLY awesome stands for your models with that laser! - MT
Edit - why does my camera warp all straight edges!!??