Displaying posts on multiple pages or as excerpts

I’m building a WordPress site that has a landing page with a brief description of the site, some images and some of the recent blog posts. Instead of using the ‘Recent Post’ plugin (I’m using now) which shows just the titles of the posts, I’d like it to show the title as well as an excerpt of the post.

I started looking at the page2cat plugin but I don’t think that’s what I need.

Is there an easy way to display excerpts of posts? And if so is there a way to do it on a page that is not the blog page? These excerpts will be on a landing page, whereas the full posts will be on a blog page.

This is what it looks like now.
This is what I’d like it to look like.