For cutting plastic computer cases, most of the time I use a regular hacksaw.
For using a dremel and cutting wheel: if it has a speed setting, use a slow speed. There are special mini-drills for hobby builders that are slower than ordinary Dremels. (they are crap for when you need torque, though)
For very fine cutting: razor-saw (serrated razorblade on a handle. See model/hobby stores)
For cutting flat sheets: The "score and snap" method: Score the plastic with a knife (do it more than once to get it deeper) and then just bend it, and it should snap cleanly along the score line. There are specialty knives that are easier to use, but a hobby knife works.
I have never cut plastic with power-saws. I have heard about people mounting the blade backwards in the machine to get a finer cut without needing a super-fancy blade.
I often do the finer work with files, and sometimes with sandpaper. When putting it together, I often used proper solvent-based plastic adhesives and I then putty to fill gaps (and blemishes). Use both coarser and finer grades of files and sandpaper for a better result.
Btw. This is my first post on this forum. I am quite new to case/keyboard mods, but I am involved a lot in Star Wars costuming and props -- and that involves putting together plastic armor.