Hosting websites W iis etc

I have been asked to host a web site. I know how to install and run IIS. I know how to Design a site. How do I connect the site cheaply to the internet? does IIS 5 also require a static IP address?

I thought about cable modems but roadrunner doesnot provide a static ip address and without that how would people find the site?

Is there a way around this? Id prefer not to purchase a router.

be specific please. any other suggestions along those lines would be helpfull.