Fist step after an installation always is to upgrade all packages including open source graphic drivers to get bugs fixed. This can be done from a terminal or TTY even if graphics are not working:
sudo apt-get update && sudo apt-get dist-upgrade
In general, for an AMD card, the Open Source
radeon driver is supported very well and should only be replace by a proprietary driver in case of issues.
If after that we still had grahics card issues we should proceed using the tested drivers from the official Ubuntu repositories accessible via System settings > Software & Updates > Additional Drivers (proprietary drivers (restricted) repository needs to be activated first):
Here shown for Nvidia
If after that the issue was not resolved we may look for a repository, a ppa or a Debian package providing a more recent graphics driver for your specific AMD card. This will already introduce a high risk of making your system instable but in case your system breaks at least it can usually be reverted.
Only if after all that the issue still was not resolved we may try our luck with downloading the bleeding edge untested newest and possibly buggy driver from the manufacturer website. This may also involve runnign a proprietary installation with a custom-made install script. In case our system does not work afte that we can not easily revert the changes we had made. So this step really should be a last resort reserved for rare cases that can not be resolved otherwise (e.g. a brand new high end card). Before you do that you should read other people's experiences, and you should also be sure that your issue will be resolved.