Yes, you can install and run PHP and MySQL on a Windows Server. As for cost, it all depends on which datacenter you go to, some are offering Windows Server at the same price as say a Redhat Enterprise based server.
Generally, if you need what Windows can provide you then the few dollars more is not going to be a big issue.
Can Windows run php/mysql just as well as Linux? or is linux considered "better"?
put it this way... both php/mysql was created for linux environments and then ported to windows.. pretty much most of the the scripts/apps for php/mysql are created to run in a linux environment.....some scripts/applications require you to run linux to work properly some just works given they were created to work with windows configurations... but to answer your question.. *nix is considered to be better to run them ....