MySQL on Windows or GNU/Linux?
There are advantages of using Linux as you base for mysql, as others have already covered, but from a performance point of view for many applications you will not see the difference particularly.

While Linux would be my default recommendation too make sure you consider your experience (and that of the people you can immediately call upon if something goes wrong). If you are familiar with Windows but have little sysadmin experience with Linux, go with Windows. Having the knowledge to fix certain things when they go wrong may prove much more important than a performance gain while things are going right, and if got know Windows like the back of your hand you may be able to tune it to the point where it performs better than a similar Linux install that you might produce. Likewise if you have a preference for or more experience with Linux go with that for the same reasons.