As the title suggests, I have installed cygwin on my Windows machine in order to try and learn about UNIX shells and kernels, and how to interact with them. I know that it is pseudo UNIX/LINUX as the actual host is Windows, but is it the best way to learn about UNIX/Linux systems?
My aspiration (which is going to be affected by the answers) is to make sure that I master the UNIX/LINUX file system commands and scripting.
apt-get
is found only on Debian-like Linux distributions, it's nothing "standard". Are you following some tutorial? Most of these are tailored to specific distributions, so you have to install those in a virtual machine—not Cygwin.