You should not update from Ubuntu to Mint. There are some differences that
could cause Mint to lose its Mintiness over time and cause your system to
become unstable. Treat them like different distributions. Download the Mint
ISO and burn it to CD and start with a fresh installation. Then your system
will be Mint and not a hybrid which can make giving advice almost
impossible.

If you install Mint from a fresh installation it will set up your graphics
card and your system should work out of the box. You should only go to ATI
if it is not working properly. In Linux hardware drivers are supplied from
the repositories. In rare cases you need to go outside, but this is not the
first choice, but the last one. The graphics driver is compiled based on the
kernel and if you get it from ATI then you will need to compile it first.
Lots of things can go wrong. This is not for the faint of heart as you need
to be prepared for troubleshooting or re-installing. You should back up and
prepare for the worst, just in case.

I should know. I have done this myself at least half a dozen times this week
trying to get Nvidia proprietary drivers to work with Fedora 12 and Lucid
Lynx. Sometimes compiling the driver is not enough and you have to edit
config files and even grub manually.