You can use pages instead of posts and have a wordpress.COM blog work like a static website, but typically it will still look like a blog since all the themes here are tailored toward blogging.
My suggestion is to go to appearance > themes in the dashboard (if you have already created a blog here) and look over the different themes and play with some of them. If you have not created a site here, perhaps create one with a name like koyannatest.wordpress.com so that you can play with things.
You will also want to review this support document on the differences between wordpress.COM and wordpress.ORG since wordpress.COM has some limitations on what can and cannot be done here: http://support.wordpress.com/com-vs-org/ .
You will also want to review the terms of service and also these two support documents which deal with types of blogs (sites) and advertising.