In general we deploy on Debian servers. I guess Debian is the most stable distribution, and Ubuntu the most easy to use. There are ready to use Debian packages (which will work on Ubuntu as well), i don't know about Fedora.
There is some documentation about installing Mendix on a Linux machine. The distribution we used for this documentation is Debian 5 Lenny.
Which distribution you should use is very difficult to answer. Mendix will run on every Linux distribution as far as i know. What you need is a web server to handle requests, Java to run the Mendix Runtime and a DBMS that is supported. The only question you should ask yourself is, which distribution is known the best by my system administrators.
Thanks for the answer. How can I get the Debian packages and how does it work?