Cutting plastic depends on the type of plastic to some degree. Acrylics can be scored and cracked, Polycarbonate is better off machined. Plastic shops can provide cutting tools for either and most such shops will cut to size and finish the edges. Acrylic material is much more brittle than polycarbonate and very subject to cracking. Polycarbonate on the other hand, scratches easier because it's softer but it is very much tougher (this what is marketed as bullet proof). Minor scratches can be buffed out of acrylics but not polycarbonate (it's too soft). Polycarbonate won't shatter and it's easier to machine but thicker materials won't yield to the scoring method unless you score them very deeply.
You might try cutting with a high-speed spiral cutting tool. They make the spiral bits for Dremel or routers. I have had success cutting 1/8 material with one. Another idea might be to use an abrasive blade in a table saw or skill saw (metal or masonry cutting blades might work) although I have cut polycarbonate with a carbide toothed blade in a table saw. You can also get abrasive coated blades for a sabre saw. You could cut the panes over sized, say by 1/8 inch and then trim them to size using a counter-top laminate tool in your router. This would remove the edge chips and finish the edge.
In any case the cut edges will benefit from machining the edges. A very small round-over bit in the router is best but a bevel edge or sanding smooth is better than nothing. Especially with acrylic material, a tiny chip can lead to the whole pane cracking right across. The machining or sanding removes these small fractures. A professional shop would flame treat the edges to achieve the same thing.
Drilling these products also requires special care. Plastic shops sell specialty drill bits but the main issue is allowing the drill bit to cut through the material. Putting too much pressure on the bit usually results in the last few thousandths of thickness to break through, leaving small fractures around the edge of the hole. These small fractures will result in a cracked pane eventually. Drilled holes should always be treated with a high speed countersink to bevel the edges. The holes don't need much of a bevel edge just enough to remove the tiny chips.
Whatever you do, wear glasses and be careful.