You can also get the Mate DE which is a fork of the Gnome 2 panel DE. It also uses Caja a fork of Nautilus 3.4 which is much better than the silly direction Nautilus is currently taking.
This will run fine. There is a repo for it and you will have to change to the version name of your Ubuntu 12.10 (I don't know what that is called).
The Cinnamon Desktop started as a set package of Gnome Shell extensions and has evolved into more of a fork of Gnome Shell. There is a package in the Debian repos for it. I would certainly not recommend using the Debian package under Ubuntu. I mention it only because it is very likely that the package is available in the Ubuntu repo. Check Synaptic for that or, as root;
apt-cache search "cinnamon"
Linux Mint Debian Edition has a very nice Live DVD that offers both Mate and Cinnamon also. It is based on Debian testing, like Ubuntu LTS versions, and is pretty nice.
It is the release I recommend for noobs.
Linux Mint, based on Ubuntu may well be very nice. Have heard very good things about it for years. It is, however, a respin of Ubuntu which is a respin of Debian. This seems somewhat silly to me.
I switched to Xfce from gnome. It is a nice DE and does exactly what I want it to do. It is what the Gnome panels always wanted to grow up to be.
Xubuntu is all right. The last testing I did for Ubuntu was Xubuntu 12.10-testing. Works good.
Xfce works better with out all the added Gnome "improvements" added by the Xubuntu team.
Debian Wheezy will be released soon (hopefully next month) but works very well and stable right now. Xfce4.8 is very nice.
Have with Xfce is the lack of tabbed browsing in Thunar (file manager). Xfce4 is very modular and I am running Thunar 1.6.1 from the Debian experimental repo and it has tabbed browsing and is very stable when used with Xfce4.8.
LMDE really only supports their Gnome based release but there is a group of LMDE users that have released a community edition of LMDE using Xfce4.10 which features even more functionality to the panels and Thunar with tabbed browsing.
Links for it are in the first post of this thread;
I have it installed on my test platform seems very nice.