In my experience Linux runs the EMU faster and more stable than Windows; however, there is a learning curve involved. There are plenty of guides on the wiki and in the forums on how to set up the server under linux and even a few posts on how to make it more secure but you will still need a basic understanding of linux in general beyond the emu in order to have a well run server.
As for which distro is the best, that is all a matter of opinion. I personally like Gentoo but I would not recommend it to someone that is new to linux as its installation process can be rather lengthy and a little involved. Debian is another good choice with great documentation and an active community. It is easy to install and you could have a server up in running in less than a day. I have tried Mandrake and later Mandriva as well as Redhat and Fedora Core, they are all good distros with extremely easy installations; however, in my opinion they might be a little more bloated than what you are looking for in a server. You can find a list of many different distro at
http://distrowatch.com with links to download each one. If you are new to linux you might want to go with one of the RPM based distros such as Redhat, Mandriva, Fedora Core or SUSE. They are all very well established distros with a wide user base and easy installations.
Well, I hope that this helps in some way.
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