Fedora is a real desktop crap OS
In the end, it doesnt matter except for what your system administrator (or hosting company if the server is managed) prefers to run as they will be more familiar with it.
There is no "best" only what is best for you. Since you don't seem to have a preference, I can only assume you have no real experience with any, so you should let your host run with what they are comfortable with.
I prefer things simple and bloat free. FreeBSD or if it must be Linux, Slackware.
FreeBSD is a complete operating system. Linux simply refers to a kernel. A Linux distribution is the Linux kernel combined with scripts and hacks etc., that the distro creator(s) thought would be best.
Freebsd if you don't have exotic or no name OEM hardware that's not supported
and don't depend on software that depends on linux only stuff....(you can run
linux shit on freebsd....but I've never been a fan of that)
Debian Linux, by far the best non bullshit linux distro....as most other linux
distros are jampacked with buggy crappy extras that you'll never use on
a server.
Won't recommend you Redhad, had many probs with it, CentOS is the best choise.
You are aware that both Fedora Crap and CentOS are RedHat based distros
if you have to use one of these...go CentOS, Fedora Crap sucks donkey balls
especially after FC3
Low cost server (hardware costs less than $50k) --> Linux
Mid range cost server (hardware costs between $50k and $2 mil)--> Solaris, HP-UX
Expensive server (hardware costs more than 2 mil) --> Irix and VMS.
As TidalWave said, what really matters is that the person looking after it knows their shit and keeps everything secure. Don't expect to be able to run it yourself.
coming from a background of network administration and security consulting I'd stay the f%$# away from Linux and Windows. Stick With Free/Net/OpenBSD. Harden the kernel and get someone on the job who knows what's going on.
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