After much tinkering and cursing, I finally managed to get Linux Container running. I had originally wanted a Fedora container, but for some unknown reason, the container would not start. Instead, I tried a CentOS 6 container, and that started up successfully, so I am using that instead. It is actually good, because I can tinker with the CentOS container, experiment with different configurations, maybe practise setting it up as a proper (i.e. no GDM) server. This will help if I decide to go for a Red Hat-themed Linux certification.
Still bugging me why the Fedora 20 container won’t start, though.