Hi Christopher, welcome to the Linux Mint forums
To be fair, you can install any other desktop environment you want on Ubuntu. But you are most welcome to install Linux Mint
The main edition of Linux Mint will not install Unity, but will (on the soon to be released Linux Mint 13) offer you the choice between Cinnamon and MATE. Cinnamon is the "classic desktop paradigm" implemented on top of modern technology offered by Gnome 3. It is being developed actively by the Linux Mint developers. MATE is a fork of Gnome 2 (which the Gnome developers have abandoned), on which the Linux Mint developers are also involved. Next to that there are also KDE and LXDE editions. But again, you can install any other desktop environment you want.
After installing Linux Mint 12, go ahead and install Cinnamon (it will be installed by default from Linux Mint 13) and you can compare Cinnamon and MATE as to which will suit you best.
Some review links:
For a bit of perspective, here is a current poll on desktop environments running on the forums: viewtopic.php?f=178&t=100787
If Unity is not for you, there should be enough alternative choices but I think you will be pleased with the main edition (Cinnamon/MATE).
Be sure also to check out the Cinnamon Spices
website for adding themes, applets and extensions to Cinnamon (and check out the Cinnamon Extras
package, which will install a lot of these for your automatically). If you haven't installed Cinnamon, see here
the most recent update for a teaser.