Steven J. Vaughan-Nichols has written a wonderful article for newbies and experienced pros alike for the sponsored site Software Quality Connection with the above title. He has lots of great suggestions and the article is well worth a quick read.
It used to be easy to pick a Web server for running your business: If you were a Microsoft shop, it was IIS, the Web server that comes as part of Windows Server; if not, there was Apache. But those days are just a fond memory now. And Vaughan-Nichols has some suggestions of lightweight servers that you may not have ever heard of, such as Nginx, Lightpd and Hiawatha. He says,"If you need website speed and you simply can't throw more servers at your performance problems, then Nginx or Lighttpd deserve your attention. If, on the other hand, you're seriously worried about attacks coming at your company through your website, then you should consider Hiawatha."