Once your download is completed burn the ISO to a CD or DVD, or make a bootable flash drive using unetbootin (http://unetbootin.sourceforge.net/
Then boot your computer from your freshly downloaded OS. If everything boot then your hardware is compatible with the OS, Once you are in the live session check for wireless compatibility some wireless cards require some tweaking to work with Linux (actually broadcom cards are the nesty ones)
If your wireless work then you should be good to go, Ubuntu includes some files in the live image for you to test in your system, there will be a folder in the home directory with a OGG file for you to test the sound and there is one for video too.
I dont know how good of suppport Radeon has in Linux I think some people with this card says the support is not that good but I really dont know.
Steam is available in Linux so chances are the games you play are available in Ubuntu. Ubuntu 13.04 is coming out this Thursday if you want to download the latest version.
Good luck to you.