Show only the category of the top post

Hello, I want to show ONLY the category of the most recent post on the index page of my blog. So whatever that top post is, it will only show posts of the same category, if you catch my drift. I see all kinds of other single-category tweaks but nothing along these lines.

Similarly, I’d love if someone had a small snippet of code to display a category-dependent masthead on the index page. Like if it is category x then it displays masthead x. I have it set up with different stylesheets right now but would prefer to just call some code using a variable instead of keeping track of all the style sheets.

Help me, good samaritans, I’m PHP inept!