A Red Hat/Fedora-based distribution that runs the 2.6.18 kernel, CentOS 5 is functionally quite similar to Fedora, but comes with a different mix of applications and tools by default. It's probably the slightly friendlier of the two distributions, so if you don't already have some experience with Fedora/Red Hat, you may want to start here first.
CentOS comes in a few different varieties. If you don't want to deal with the 3+ GB .ISO, there's a live CD -- although the only installation option for the live CD is an over-the-network installer. Be sure to take notes beforehand about where to fetch the files from, as there are no default download locations available in the installer. There's also a separate network-only installation CD (a mere 7-MB ISO), but again you need to supply the address of a repository.
The installer is also extremely similar to Fedora -- the same prompts and behaviors are all there -- so if by chance you've cut your teeth on Fedora already, this should be familiar territory. Newcomers will need to understand disk partitioning and the like, but the package choices are kept mercifully simple. Other changes are subtle, like the additional feedback you get during the boot process.
Most of the software in CentOS is also similar to what you get in Red Hat; for instance, Red Hat's SELinux policy tool is also installed by default -- although it's configured in the Security Level Configuration applet instead of as a standalone program. That said, some of the applications in the default repository for CentOS are not as recent as what you might find in other distros, presumably because these older versions have passed QC by the CentOS team. The highest available revision of Firefox was 220.127.116.11.; likewise, OpenOffice.org didn't have anything newer than 2.0.4. The same seems to go for the server / development tools: the latest revision of MySQL is 5.0.22 (as opposed to 5.0.51a for the official release).
I expected hardware behavior to be pretty much the same on CentOS as it was on Fedora for all the systems tested, but there were a couple of exceptions. The VAIO's widescreen display came up properly right out of the box, but its wireless card (an Intel 2200BG) wasn't recognized. The Thinkpad, too, had trouble booting, probably due to its display hardware. Consequently, you may want to try the live CD of CentOS to determine what kind of hoops you'll have to jump through to get everything working.
As predictable as this may sound, Ubuntu 8.04 remains one of the best desktop distributions for many good reasons: it works with almost any hardware you throw at it, and has tons of features for both existing Linux users and prospective converts from Windows. openSUSE fared better on desktops than notebooks, but has a lot of organizational ideas in its interface that I'd like to see expanded on in the next release.
Fedora and CentOS may have both been derived from a common source but were dissimilar enough to be considered separately: Fedora recognized a slightly broader range of hardware, and CentOS seems a bit friendlier to newcomers and includes a broader spate of preinstalled administrative apps. Finally, Mandriva and its cousins -- SimplyMEPIS and PCLinuxOS -- all get major points for ease of administration, although each one organizes things somewhat differently. What you expect to find in one, you may find in a totally different place in the other two.