You can do either, it’s up to you depending on how invested in your static site you are and how much work you want to do transferring things over.
The Codex page on Integrating WordPress with your website outlines how you could have WordPress installed in the /blog directory, and show recent posts on your static site through the use of a bit of php.
Your other option is to have WordPress take over serving all of your site’s content. It’s pretty easy to set up a static home page, plus contact, etc., as well as a blog at whatever url you choose. See the Codex page on WordPress Settings > Reading. You just need to create two pages, then designate one your home page and the other to be the page that shows your posts.