If you included more details about the hardware, you'd get better advice.
That being said, a quick Google shows it is a very powerful and modern laptop. You should be able to run any Linux distro with ease! Here is a good comparison of the 10 most popular:
Personally (this is just opinion) I think Arch is a terrible choice for this scenario. It is a "rolling release" distro which means it gets updates every single day that may, or may not, break the system. A popular distro for Linux hobbyists, but a terrible choice if you need to keep all 30 machines going reliably. Better to choose a very stable distro, like Debian, CentOS, Ubuntu LTS, etc., that will give you several years of support with minimum upkeep.
ps I would recommend visiting ubuntuforums.org and seeing if you can find an answer to your "kernel panic" problem. I find it hard to believe Arch will run and Ubuntu will not (especially since Dell and Ubuntu are business partners); maybe it is as simple as using the LTS release (10.04), setting an appropriate kernel option during boot, checking the CD for burn errors, etc.