Personally, I'm not a big fan of PPAs for graphics drivers.
Each version of Ubuntu has in its repos the most recent ATI driver at the time of the release. That was 12.4 when 12.04 came out. The easiest thing to do would be to just use that driver.
If you don't want to do that, you can download the driver from ATI and either: 1. Make it into a .deb; 2. Run the .run file raw.
The broad answer to your question is that the drivers are available and are, despite common misconceptions, quite easy to install. I'm not sure where the "ATI's drivers are hard to install" myth comes from.
From the repo:
sudo apt-get install fglrx fglrx-amdcccle
sudo apt-get install fglrx-updates fglrx-amdcccle-updates
or, if there are multiple ATI cards
sudo amdconfig --initial
Two commands. That's it if you install from the repo.
sudo amdconfig --adapter=all --initial