Cue 100 replies with 100 different suggestions...

You mean "Distribution", not "Brand", I am fairly happy with Fedora Core 4, though I installed a Gentoo recently, and though it is harder to set up is much more customizable.
A coworker of mine thinks Debian is the best ever (he despises RedHat Clones), I think it is pretty good, though I dont see how is it any better than Fedora.

The distribution I use is Ubuntu.

Moving this to Everything Unix.

If you are new to linux than Mandrake, SuSE or Fedora are good choices. Once you are more comfortable with it a lot of users use some of the fancier versions like Gentoo and Debian. Distrowatch usually has some good information.

I'll say that IMO Gentoo is great if you know what you are doing. It's amazingly simple to install almost any software which is a huge advantage when you are building it to play around on and expirament with different things.

I love it so much even my XBox runs a flavor of it.

Slackware. It is the newbie distro in that you go from newbie to linux-savvy.

1. Print or write down the names of all Linux distributions you can find on a sheet of paper. For completeness, add all free BSD variants.


2. Tear up the sheet such that each piece has a single name on it.


3. You have several options here:
   
   1. Place all the pieces of paper in a hat/other large container, dip your hand in and randomly pick one;
   
   
   2. Place all the pieces of paper on a dartboard (or appropriately large surface) then throw a dart/shoot an arrow/squirt a watergun/fire a paintball gun, preferrably blindfolded, and consider whichever one your dart/arrow/water/paint pellet strikes as your selection;
   
   
   3. Throw the pieces up into the air like confetti and try to catch one as they come down (warning: this method requires cleanup), which will be your selection; and so forth...


4. ...


5. Profit.

The moral being that, for a server which doesn't need to run the latest, most cutting-edge software, which doesn't need to run arbitrary applications (you can compile all your binaries for it) and doesn't have any other stated special requirements, it really don't matter which distro you pick. Just pick one.

Happy hacking.

Fedora is bloated for Linux standards. This is not neccessarily a bad thing. This means you get everything. In the end which distribution of Linux you choose is irrelevant because you'll get it to work either way, but I suggest new Linux users use something Fedora because it works pretty well for desktop usage. What I mean is a lot of documentation is written for a machine running Fedora or Mandrake, which has the characteristic of having pretty much everything setup for you. I personally have a lot more experience with Fedora. It would probably be easier to start there.

Let me give you an example.
MythTV is a PVR program that runs on Linux 2.6.x. Lets say you want to setup MythTV on your Fedora box. There is a website completely devoted to getting MythTV running on Fedora. http://wilsonet.com/mythtv/

My point is there are subtle little nuances that experienced linux users can pick up on that you are expected to know because lets face it...Linux was designed for hackers. RedHat has dones pretty well in creating a newb proof environment, but you can still muck up your system pretty bad if you don't know what your doing. For example...
"cat /dev/random > /dev/hda"

cat reads a file.
/dev/random is the linux random number generator.
> means pipe output to file
/dev/hda is your hard drive device file.
I'll let you figure out the rest.

Fedoras installation is simple enough for a average desktop user to understand without any previous knowledge.

Debian is more of a joint effort of the debian community (bunch of linux gurus) and Fedora is mostly sponsored by RedHat.