Perspex and acrylic are both names given to a material called PMMA. It's more brittle than most plastics, so you need to take a bit of care when drilling and cutting it, otherwise it chips and/or can crack under extreme working.
Polycarbonate (also known as lexan) and PVC sheet is close to industructible, the former is a lot more expensive, but transparent and a little tougher than PVC (not that we require that level of strength). Very different working characteristics to PMMA, the plastic is much softer, not brittle at all. Therefore it's easier to work with hand tools, coarse cutting blades etc. as it won't chip.
On the downside it doesn't polish as well, and is more easily scuffed, also it's slightly less rigid, which means it will deform easier under pressure. I find it easier to get a very smooth turned finish on PMMA than polycarbonate and PVC. Also the rigid nature of PMMA means it tends to hold a machining tolerance better.
However once again for our applications we don't need to worry too much about this sort of thing.
So in a nutshell any of the above plastics work well, PMMA needs a more delicate touch.