Performance wise most Linux choices will be similar. More important considerations are which version of mySQL you need (if something recent is required, some distros like Debian/Stable may be too far back and if something very recent is required then you'll need to hand-compile), long-term support for security updates, and your familiarity with that Linux flavour.
Off the top of my head my recommendation would be either Ubuntu/LTS Server (i.e. 10.04) or CentOS (the most recent major version) as they have official security patch support for longer in the future without needing to completely upgrade the OS, with Debian/Stable usually not being a bad choice either. I'd go with Ubuntu or Debian myself as I am more familiar with Debian style setups than RedHat ones.
What-ever you go for refrain from installing more than you need - i.e. don't bother with a desktop environment.
Once the base OS is installed, assuming the mySQL build offered in the standard repo is sufficient, running something like
aptitude install mysql-server (Debian/Ubuntu) or
yum install mysql-server is all you need to do to install (using the distro's default packages like this makes keeping up-to-date with security releases easier as you can just do something like
aptitude update && aptitude safe-upgrade (Debian/Ubuntu) rather than needing to rebuild the latest version from source or obtain and install binaries from elsewhere.
Once installed you will find the configuration files under
/etc. The content of these will be almost exactly the same as for Windows and significant differences tend to be well commented in the files themselves (at least in Debian's case, though I assume this is the same elsewhere as the bulk of the details probably come from the sample config files in the official mySQL documentation and/or source) - so if you are familiar with configuring mySQL on Windows this should offer you few (if any) surprises.
Edit: having time to familiarise yourself with the setup (as per your response to Bloodphlia's concern) is very much a good thing - I wish there were far less servers out there installed by people who did not have time to experiment and learn first! If you can find the time I suggest installing a couple of systems in virtual machines under vbox or similar. You can use these "throw-away" VMs to play and see which Linux variant you prefer and to test things out in an environment where you can experiment in detail without fear of upsetting a production machine.