This depends largely on whether having a super up-to-date system really matters to you because many distros are very stable once configured and only have problems with updates. I really like arch and once it is set up it is very stable; however if you feel the need to constantly update your system it might break occasionally although in my experience such breakage can normally be avoided if you check the arch site and forums for any major problems with new packages before updating. If you only update a system when you really need to then you should not have to worry about reliability too much.

Stability is affected by what desktop environment you use, not just what type of distro. CentOS is stable. Mint with KDE or LXDE is fairly stable. Xfce seems to be a bit more buggy then some of the other desktops. Gnome also freezes on occasion too. I've used SuSE before and it seems to freeze up a little more then either Fedora or Mint does. Generally its fine.

If stability is the biggest concern, try PC-BSD. I use it on an external usb hard drive. The standard DVD installer works fine with no modifications so long as you select the external drive as your target and not the hard drive in your laptop by accident !! I'm not sure if the external USB drive would behave normally if hooked into another computer, however. It is a backup system in case my primary hard drive dies suddenly.

Make sure that you run as much RAM as you can afford or max out the machine. Don't neglect to install the fastest speed RAM supported by your system as well.

If they have over 1gb of memory, then KDE may work okay, so would Gnome 2 but it's going away sometime in the future.

SalixOS (based on Slackware)
Mageia (using a lightweight environment)
Linux Mint(using a lightweight environment)
Debian Stable (using a lightweight environment)

On my AAO, I currently use Mandriva 2010.1 with Gnome 2 and it runs good, but may switch to Mageia with Xfce4. I've also ran Debian Testing on it before I switched to Mandriva.

I currently run SalixOS & Mageia G2 on my desktop.