Welcome to Ubuntu, I am unsure of your graphics with AMD but it might have to do with Unity is graphic intense on hardware. Probably Xubuntu would work better for your needs as xfce desktop uses far less GPU then Unity. Also install the "Ubuntu Restricted extra's" in the software center as those will ensure you get all your codecs for video and audio playback.
As for Firefox and Flash, Adobe no longer supports Flash for Linux. SO the one available for Firefox is a older flash plugin and I would recommend using Chrome as it has built in flash support. If you prefer to stay open source as possible then install Chromium and then install the pepper plugin in terminal with these commands....
For Ubuntu and flavors 12.04 - 13.10
Code:
sudo add-apt-repository ppa:skunk/pepper-flash
sudo apt-get update
sudo apt-get install pepflashplugin-installer
Code:
sudo apt-get install gksu #it`s not installed by default in Ubuntu 13.04
gksu gksu gedit /etc/chromium-browser/default
For Ubuntu and flavors 14.04
Code:
sudo apt-get install pepperflashplugin-nonfree
Code:
sudo update-pepperflashplugin-nonfree --install
Bookmarks