Ubuntu is a great distro and I would highly recommend it. It's user friendly, and Debian based.
It is very easy to get your card working in Ubuntu. You need to open the synaptic package manager, then enable the restricted repositories. This repository contains 3rd party drivers from nvidia among other things. Then you need to install the package nvidia-glx-96
This package has an info page here
Once you install the correct driver you shouldn't have any problems.
Note that Linux Mint is Ubuntu based, so this same solution will work with Linux Mint as well.