You can run any version of Ubuntu you want on a Toshiba Satellite Pro L830-15K laptop.
In order to install the correct graphics driver for your laptop, open the Ubuntu Software Center and search for ATI binary X.Org driver. You can find this package the easy way if you just search for amd. From the ATI binary X.Org driver description in the Ubuntu Software Center:
"Video driver for the AMD Radeon and the FireGL graphics accelerators. This package provides 2D display drivers and hardware accelerated OpenGL."
From my own personal experience on hardware similar to yours, I would say that you should expect splendid graphics performance from the ATI binary X.Org driver. There are also slightly more up-to-date versions of the same driver available at the AMD website, but I stuck with the ATI binary X.Org driver package that I installed from the default Ubuntu repositories, and I have never had any problems with it.