Hi Karl
i'm a bit late coming to this but hopefully i can help. Hereis a photo of a perspex case I made about 10 years ago when my son wanted to keep some stick insects:
It worked - no stick insects escaped.
the perspex was from B&Q and about 3mm thick. We tried various ways of cutting it, such as a band saw, or jig saw. In the end we found that scoring it with a very sharp Stanley knife 4 or 5 times allowed it to snap. If in doubt score more than you think you need to!
I am not convinced it would be easy to get nice clean edges so used 'L' shaped wood for all of the corners which hid the edges of the perspex. My other hobby is woodworking so I made these form some old oak I had, but diy shops such as B&Q have a large stock of "L" shaped wood.
The 'proper'way of building it would be to make the wooden frame and then add the perspex glazing. I cheated and glued the perspex to the wood as I went so that the perspex is a structural part of the case. the process i would use for a rectangulae case is:
1 - cut out all 5 pieces of perspex
2 - cut four lengths of wood and glue them to the rear side piece of perspex.
3 - cut the 3 lengths needed for one of the sides
4 - glue the pespex to one end of the rear piece already made
5 - add the other 3 pieces of wood
6 - repeat steps 3 to 5 for the other side, the front and top.
for the base I used some plywood edged with some wood so that the above-made top can fit inside it.
one thing to remember - each corner is a 2-way 90degree corner and both edges need to be cut before gluing the perspex. It will be a whole lot easier if you have a 45 degree mitre block and a good sharp saw.
Peter