Ubuntu 12.10 is arguably the worst of Canonical, you're much better of with 12.04 LTS if it has to be Ubuntu.
However, Ubuntu is arguably not the most representative of the quality/stability/security/userfriendliness of GNU/Linux. It's a lot like Windows in many aspects, relatively old and relatively slow.
On an older machine, you'll have much more fun running a fast GNU/Linux distro, like Arch or Slackware, but those two in vanilla form are pretty hard to handle for a user without experience. A Pentium 4 is still a pretty fast machine for Puppy Wary, if you like Puppy Racy that would be an alternative, but a P4 is plenty fast for a modern full functional state of the art GNU/Linux distro like Manjaro Linux for instance. Manjaro is the rising star of GNU/Linux, the standard version comes with XFCE, which is nice and fast and full-featured, but you can also have other desktop environments if you like, as with all GNU/Linux distros.
Manjaro is based upon Arch Linux, so it has the benefit of being a rolling cutting edge release (without the downsides of Arch itself because unstable packages are filtered out because they use their own repos), it has a vivid community, it is fully compatible with Arch and the AUR, which contains an incredible amount of software and is really easy to use.
Since Manjaro version 0.8.2, it has been thriving, and is considered a must-install on both somewhat older and less capable machines for a speed upgrade, and on modern machines for supersonic speed, and it just looks good and works out of the box. By the end of this year, they plan on coming out of beta, but in reality, this distro feels less like beta than Ubuntu 12.04 LTS, and it just flies on older hardware or netbooks. The install assistant has much less graphical bling than Ubuntu, in fact it's only pseudo-graphical, but it is very easy to use and a lot less confusing than Ubuntu.
However, if you want the best of GNU/Linux, (maybe it will run fast enough on your older PC, you could at least try it) get Fedora 18 with the standard Gnome Shell, and install Fedora Utils and get some Shell Extensions. With Fedora Utils, you can install some expansions and necessary software and do some maintenance and setup fully automatically, fully within a GUI, and in only a few minutes. The combination of the bleeding edge features of Fedora, it's stability, it's professional community, it's backing by Red Hat, IBM, Intel, etc, with the added ease of use of the new Anaconda installer (easier than a Mac), the great Gnome Shell 3.6 (much better than any Mac or any Windows), the Linux kernel 3.8, the great Fedora Utils application, the best package manager of all GNU/Linux distros (Yumex aka Yum Extender), it's legendary security, and it's endless compatibility with various hardware, is just ultimate win in my opinion.
