That being said, if you insist on C++, Visual Studio on Windows, XCode on Mac and KDevelop on Linux would be my IDEs of choice. On Linux and Mac most people use vim or emacs though. Libraries to look into would be the standard STL and Boost. Qt or wxWidgets for GUIs.
COBOL? I'm sure you can run it on a modern computer, hell, my iphone is an order of magnitude more powerful than the mainframes from 30-40 years ago... but in the name of all that's good and holy, why would you ever want to do that?