So, you’re going to install WordPress and looking for the right kind of server to install it on. I’ll save you a little time, get a Linux server.
Yes, WordPress will install and run just fine on a Windows server if you keep things basic but you miss out on a lot of fun, easy things going that route. PHP is also native to Linux and run better on it. Since WordPress is PHP based, it will run better and more efficiently on a Linux machine rather than a Windows machine.
How much hosting power do you need? Well, how many visitors will you have on your site and how many extra plugins and high usage pieces will your theme have?
Basically, you don’t need to worried about being on a shared server. You certainly don’t need your own dedicated server unless you expect tens of thousands of visitors a day. That would be a GREAT problem to have though. But at the same time, you don’t want to be on a shared server with 1,000 other people and have it take forever for your site to load for each person. That gets annoying.
Find out from your hosting provider what kind of specs you can expect. If you’re paying for the “GoDaddy Special” at $5 a month or whatever it is, expect to have really slow load times and problems with your server. Pay for quality and get something better. Just steer clear of a Windows server and go Linux. It will make your life much easier in the long run.