Here is a good place to build a pc part list. It will also let you know on incompatiblility issues and such of your build (if there are any). Also recommends sites to where to buy each part from lowest price to highest.
Well it depends on the build. Like for example the video card. Some of the newer video cards won't fit in mid-tower cases and such. So it would be hard to just tell you which case to pick and it doesn't work with the rest of the build.
It is the cheapest case I can find. I doubt you will find a case for $50 unless it is a extremely tiny case like the Mini-ITX which some things you have in the build may not fit in the tiny case.
I would prefer suggesting you to get a case with air fans attached on both sides. This will help to keep your CPU cool and work long hours without interruption.
If you want something high-grade at a medium price range, look out for Fractal Design's Define R4 or R5. It comes in non-windowed and windowed versions, and is available in black, gray and white. Materials consist of steel and plastic.
If that model is out of your price range, then Fractal has other cases available.