include individual wordpress articles on separate website

I have a client that I built a static site for a while back. They are now getting into using social media and are asking for a blog and news publishing platform. I thought WordPress would be perfect for both of these features. What I planned on doing was setting up their blog with two categories: news and blog and having separate wordpress pages for each. That’s all easy for me to setup.

The trickier part for me is that the client wants to keep the static site intact and add a place at the bottom of the homepage where excerpts of the newest blog post and the newest news story would be shown, both linking to their respective articles in wordpress. I thought I could do this by simply pulling directly from the wordpress database but the category names are not part of the wp_posts table so I cannot (don’t know how) to pull only the latest post from a certain category.

Can anyone tell me the easiest way to pull this off?

Thanks in advance.