Category Display

I’m trying to create a header that pulls data from the most recent 3 posts in a specific category along with pulling the image associated for the most recent post (if there is one) to display. I can create the styling just fine, but I don’t know how to reference and pull the post information. I don’t want to do a loop because I don’t want all posts.

I’m thinking of something along these lines.

POST IMAGE (overlayed with the title of the most recent post of a category, which is a link to that category, possibly referencing the date and time of the post)
Under that, I want to put just text links to the post just prior to that within the category followed by a third link to the post prior to that one.

Are there specific tags to pull post titles and perhaps small post excerpts and display them like this?