"Linux" is common name of operating systems based on Linux kernel. The Linux kernel and other free and open components together make lots of systems combinations. That's why there're no "official" Linux OS. Linux kernel and a pack of software for different purposes make a distro. There're lots of Linux distros for different purposes, but most of them are based on few basic distros: RedHat, Fedora, OpenSUSE, Debian, Ubuntu, Gentoo, Slackware and so on.
The majority of Internet servers use Linux OS. And there're reasons for it.
So, if you do not need some OS-specific software, it's better to choose Linux hosting, besides it's the cheapest solution.
If you are using the shared hosting, you cannot make the hoster to install the system you want for you.
But if you are VPS/VDS or dedicated server client user, you're free to choose the system.
We recommend to use 32-bit (i386, i686) distros on servers with less than 4 Gb memory. The reason is that you need more memory to store data structures in 64-bit (x86_64) systems.
RedHat Enterprise Linux is designed for corporate users and you have to pay for the distro (with or without support). But due to GPL (GNU Public License), system source code must be provided for free. So, there's a free distro called CentOS, that was made of RHEL source files. Besides, there's Fedora distro, maintained by RedHat and community. Fedora uses the most fresh software and just after Fedora the software gets to RHEL. By the way, Fedora is totally free.
Debian is considered to be one of the most stable and universal distros. Debian supports wide variety of architectures and has the largest software repos for Linux. There're many Linux distros based on Debian. Some Debian distros are using not just Linux kernel, but also GNU Hurd and FreeBSD kernels.
In general, choosing the Linux distro is almost a "religious" question. If you don't have any specialized tasks, choose the distro for what you have system administrator for the server setup. For example, we are using Fedora.