My personal favorite choice is Slackware. It's one of the most, if not the most stable and secure Linux distributions out there. It's the oldest Linux distro still being maintained and updated. That being said, in order to be so stable and secure, by default, even on the newest release of slack, the default kernel is 2.4 based rather than 2.6 based. Also, Slackware doesn't come with the apt-get package management software. There are alternative versions out there that work with Slackware packages, but none of them are as good as dealing with dependencies as apt-get.
Given the options you listed.
Suse isn't bad, Debian is not bad either.
I have limited experience with SUSE, however, the mere fact that it was originally based upon Slackware is a big plus to me. It was initially just supposed to be a German language translation of Linux, and it grew from there. SUSE seems to be focused on being more user friendly and at having lots of handy workstation utilities. For a server, I'd run Slackware way before SUSE, but for a regular desktop PC running Linux, SUSE would be a very solid option.
With Debian, you have access to IMO the best package management system. Debian has a very large user base currently, and it's been ported over to MANY architectures.
Debian, like Slackware, has somewhat long release times on the stable branch, where upgrades/updates are usually only done for security reasons rather than getting the newest or coolest toys. Because of this, Debian is a very solid choice for a server but not so solid for a workstation. The Distribution has been around for a very long time, and like Slackware, Debian has a very solid reputation.
Fedora is based on Red Hat. I have ran Red Hat 5, 6, and 7 in the past.
I've seen Fedora Core through Fedora Core 4 boxes, and I personally don't care for it.
I don't like how the Red Hat RPM system is set up. Dependencies are a pain to deal with. Red Hat uses unconventional paths and filenames for a lot of various config files, the installer is "easy", but it generally results in leaving LOTS of holes open right after the install.
Red Hat 5 and 6 were really good, with 7 and beyond, they really lost a lot of respect from me. It seems like in their attempts to cater to the lowest common denominator, they sacrificed too much end user decision resulting in a less secure and harder to configure box. (Harder to configure, because conf files aren't in the same place as many other distros a lot of the time)
Out of the three Linux distros you mentioned, a properly configured Debian server will likely have the least possible amount of loopholes or undiscovered exploits. It will run the most stable, and it will be the easiest to patch for security. It won't have all the newest bells and whistles, but it would make for a much more "solid" server than Fedora or SuSE.
Others have mentioned Ubuntu. It is based on Debian, it is generally updated a lot faster than Debian, and it too uses apt-get, so it's a very nice distro as well. I'd stick with Debian on a server over Ubuntu, but I'd use Ubuntu on a workstation over Debian. Since this is a Web Server, Debian would be my pick between the two, but it's close.
In conclusion, my bias forces me to vote for Slackware
PS, n0cmonkey might have a cow if he sees this thread with no BSD recommendations, so I'm also going to say, read up a bit on OpenBSD, FreeBSD, and NetBSD. I have very little experience running BSD on my own boxes, but I use OpenBSD and FreeBSD boxes at work every day, and they are VERY solid servers. Consider all your options and pick the best.
EDIT: Wow, I didn't realize how long and boring my post is, my apologies for such a long post.