You can machine polycarbonate and acrylic with woodworking tools. Just drill it slowly and use a drill press and a machine vice, when drilling the edges.
Cutting a thread in both materials works very well, so you can use machine screws.
I personally prefere polycarbonate because it is stronger and bends instead of fracturing when stressed. It's much more expensive though.
Be aware that both are thermoplastics. It is easy to heat parts of the sheets (for example with a constantan wire) and bend them. That might be an attractive alternative to screwing parts of your case together. On second thought bending might not be a good idear if your powersupply can get really hot, because the sheets might unbend themselves then.
Both materials should be maschined with their protective sheets. Removing them should be your last step, exept if you heat them, then you should remove the protective sheets before heating because otherwise they burn into your acrylic or polycarbonat.
If you want perfectly transparent edges use first a scraper, than sand with 280 grade grit-paper or directly wet with 600 grade grit-paper. Depends on the quality of your scraping (Does this word exist??).
For bending, acrylic is easily bent with a hot wire setup - gives nice crisp straight bends and will not unbend with heat (you have to hit the melting point of the acrylic, but if it gets that hot, you have other problems)

As for clear edges, two even easier solutions are
1) blow torch. Hotter is better - MAPP works well, but regular blowtorch for plumbing works nicely too. Just take a few scraps and get a speed and distance worked out and it's easy to do. This is how the pros do it.
2) MEK. The MEK dissolves the acrylic, so some MEK on a rag wiped over the edge will instantly melt the edge and make it clear.
The big problem with polycarbonate (besides price) is that it gets destroyed by UV light. It goes yellow and brittle over time, whereas it's not really much of a problem with acrylic.
If getting pieces laser cut, it is easy to have interlocking tabs put in the pieces (sort of like a dovetail joint from woodworking). MEK is usually applied with a syringe and capillary action draws the MEK into the bond line. Squeeze the syringe until a drop starts to form and then touch it to the bond line, and it will get sucked in... hold for several seconds and you have a welded together piece that will be extremely strong.