It is not as simple as choosing the hosting platform that matches your operating system.
Indeed for most users Linux hosting could well be the best option even if your computer operating system is windows.
Choose Windows hosting if you want to use microsoft products like Microsoft Office or Front Page - the microsoft website design program to produce your website. Windows hosting should be used if you have to use a MS SQL Database or use ASP for interactive pages. For a simple website without need of a database or interactive pages this does not really matter and you might prefer to choose on cost alone - although Microsoft hosting can be more expensive than Linux.
Linux Hosting has a reputation for stability and ease of use. Because it is open source software many indepemdent developers are worlking to improve it. Also there are many free or open-source scripts available for things like customer response forms that work with PHP. There is also support for the open-source database system MySQL. Hosts often allow more MySQL databases than MS SQL databases on an equivalent windows hosting plan.
Linux is particularly suited to on-click install applications like Wordpress, Dupral and Joomla.
Finally Linux hosting is often cheaper for an equivalent Plan. Check out the One and One Windows and Linux hosting plans to see the similarities and differences.
So Unless you specifically need to us Front Page Extensions, MS SQL, ASP or other Microsoft specific technologies to tie in with your existing software you can usually find a Linux alternative at leaset as good and cheaper.