R9 280x should run fine on Ubuntu 14.04 with the fglrx 15.12 drivers - but I think you have to manually download them and install, I don't remember them being an apt-get options anywhere offhand.
I am running fglrx(0): Version: 15.20.3 which was installed from the additional drivers menu in the Xubuntu 14.04 GUI.
I'm pretty sure that's the 15.7 drivers - fglrx 15.12 drivers identify as 15.302.something or some such.
I don't have access to any of my LINUX boxes to check right now, as they're all in my new place and I'm typing this from my old place.