Marsh: First of all keep in mind there are two kinds of clear synthetic material made into sheets. when you say acylic I think Methleacrylate aka lucite. plexiglass and perplex. the later development is polycarbonate plastics.
there are two methods of cutting you can saw it like wood or metal or you can score and break like glass.
I have a friend that has made many case for his models and he uses a trim bit in his router to trim to size and get a clean edge.
You need a smooth edge to effectively fabricate it exposed edges need to be polished . i use 320,400, 600 grit silicon carbide paper then auto finishing compound and plastic polish. edges to be welded just need to be smooth and straight. they can look a bit frosty .
the best way to attach it to itself is with a chemical weld set the pieces in place and use a n applicator similar to a syringe needle and the capillarity action draws in the fluid and welds it in place. use caution , gloves and ventilation (outdoors as the solvent is nasty) a place I work bottles it they use positive pressure environmental suites in a negative pressure isolation room. Dichloromethane (methylene chloride), which is obtainable in paint stripper, can solvent weld polycarbonate and polymethylmethacrylate.
Take care with the solvent if it drips and runs it will leave tracks that are hard to get rid of.
this is the stuff we used at the model shop I worked in :
Here in the US any good hardware store or home center caries plastic sheet stock. and yes I see yo are in the UK .
Tin