I am running GNU Emacs on Windows so entering:
M-x shell
launches the Windows command-line DOS shell. However, I would like to instead be a
I'm using EmacsW32. C-h a shell$ gives a list of shell launching commands and the commands cmd-shell and cygwin-shell look interesting. Both commands need EmacsW32. They are also found in the menu: Tools > W&32 Shells.
If you run cygwin-shell for the first time, and if you have not setup cygwin path in Emacs, it leads you to the Customization page where you can setup the cygwin path by pressing Find button.