So it sounds like you've got everything connected correctly. When you go to your browser, it should take you directly to a Comcast sign up page where you can fill in those details. If that is not happening with the current set up, you might want to give Comcast a call.
In direct answer to your question however, yes, it is best practice to have a router between your home network and the internet to protect you better than the software firewall built into Windows can.
I hope that helps. You don't need the router to make the current setup work, it's just recommended to protect you. If you are still having issues, I would call Comcast to make sure things are set up properly on their side.