For a simple static website, it really does not matters which platform you choose to host your website on, however I recommend Linux. With Linux there is a lot more Open Source software (free to use) available, with Linux, you can add more features to your website in the future.
I will choice linux all the way,
it's faster and have lot's of software and options for free.
windows license is expansive, windows need many many hardware resources and have lots of software limitation and software cost a lots.
Selecting between Linux or Windows hosting also depends on the applications that you are going to use on the website. For instance, if you would like to use ASP.NET, then you will have to opt for a Windows hosting package.