WP Website and Blog

So I was all happy coding along then my client drops this on me.
They want to be able to have a blog section on this WP site in addition to the Website portion.

I’ve been using pages so far to build the site, with index.php as my home page because it has radically different styling/structure.
I use the page.php for other pages.

Now I started looking through and am not sure how to do this next part. I want to add a new section on the site for a blog. I don’t want any of the content on the home page right now but want a link they can click and go to the blog section to view posts.

I’d like to set it up to show the latest 3-5 entries and just title of the others. I’d also like to add search to this portion of the site.

But for now I’m just looking for a start, where do I begin to add a blog within my WP site.

Thanks for your input, community, you’ve been great!