Please take a look at http://www.cpu-world.com/CPUs/Bulldozer/AMD-A10-Series%20A10-7860K.html , from where the Radeon R7 graphics core could be confirmed onto your processor. Desktop , from this link, the latest crimson driver is 15.12, for Ubuntu 14.04.2. Because it is proprietary driver, closed source, so it is hard to adapted to support current version of Ubuntu.
There are thousands or more Linux distroes, the most popular and easy to use, in my own experiences are Ubuntu. And so many OEM manufacturers, such as Dell, preinstalled Ubuntu on selected models of computers. Ubuntu suggested users to use open source driver, so you have not to care about the problem of drivers, because it is already integrated, or downloaded from Internet when installing Ubuntu automatically.
I wish have a good journey of Linux accompanying with this wonderful processor!