I see people have already recommended RHEL and CentOS. Those are the two most common Linux VMs being deployed in enterprise clouds right now.
I use Xubuntu (an Ubuntu distro that uses XFCE instead of Gnome/KDE) and Fedora. Fedora is basically the non-enterprise build of Red Hat.
I wouldn't recommend Mint since it, as AustinChief said, is basically a pre-packaged GUI aimed at user-friendliness. Not a great learning platform as it hides much of the "guts".
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