[Off-topic] SciFiSurfer:
Well, I don't know what Slackware's release cycle is, but 13.1 came out last May. It's nearly a year old now.

Fedora 14 is the current version, and (when my PC is actually functional) it works extremely well. You will want to refer to:

mjmwired.net: Fedora 14 Personal Setup Guide (this covers almost everything you need to get started);

mjmwired.net: MPlayer - Fedora Guide (this gives you the process of D/Ling, compiling and installing the LAME encoder, amongst other useful things); and

The Unofficial Fedora FAQ (which is another excellent resource for answering questions and setting things up, but I'd start with MJM's stuff first).

Ubuntu has two simultaneously-current versions: 10.04 LTS (which means it is the Long Term Support version that many businesses and individuals standardize on and is good for 2 years) and 10.10, which is the most current 6 month release version. Ubuntu releases in April and October of every year, which is why you get x.04 and x.10 version numbers. You will want to refer to help.ubuntu.com: Restricted Formats and I would also recommend going into the Synaptic Package Manager and installing all three of the following: Ubuntu Restricted Extras, Kubuntu Restricted Extras, and Xubuntu Restricted Extras, because each has a couple things the other doesn't.

As far as "which would I recommend", that's a really wide-open question, and I guarantee as others weigh in here, you will get a LOT of varied opinions from people. In general, I would simply tell you this:

Ubuntu is based on Debian's core components. Debian is noted for stability and wide ranging hardware support. Canonical has done a really good job adding a lot of "spit and polish" to this, and it is actually a very good distro, but they have rubbed a good portion of the existing Linux community the wrong way because of their "embrace and extend a huge tent" philosophy (the objection here generally being that the Linux community really doesn't want a bunch of "Windows idiots" and "Mac OS X idiots" as members) and because they have often not contributed their enhancements and other development efforts back up to the project sources they're using (this is referred to as "contributing upstream") like they should have. Nevertheless, Ubuntu does have a lot of positive things to recommend it.

Fedora, which is actually a spun-off project from RedHat, is amongst the older distributions, and is somewhat more cutting-edge than other distros, such as RedHat itself, or Ubuntu, etc. It is an RPM-based distribution and has one of the largest communities of users out there next to Ubuntu. It is renowned for contributing upstream and is a good and reliable distro. However, as you can see from the list I posted above, you will have to do a LOT of extra initial configuring work because Fedora's philosophy is to ship with pretty much only F/OSS components. Though they certainly don't prohibit or flat-out discourage their users from adding in other non-F/OSS components, such as commercial 3D graphics drivers, video/audio codecs, etc., they don't include them.

Whichever you decide, good luck!

Oh, and one more thing: Whichever you go with, become a member of the associated message board (Ubuntu = ubuntuforums.org; Fedora = fedoraforum.org; etc.) because there is a WEALTH of information and WIKIs and many many many questions already answered.