Is it more or less expensive to host my site on a Unix or a Windows platform?

That depends on what you mean by “hosting your site”. If you plan to host the site yourself, and you own the web servers or the software on them, then Unix (or Linux) would definitely be a less expensive option. If you plan to sign up with a web hosting company, and they own the servers and the software installed on them, you will find that there are excellent hosting options available for each platform at very comparable prices.