The greatest thing about WordPress is the fact that you can pretty much do anything you want with the look and feel if you're willing to put in the effort to do it. If you had a look that you were happy with, you can likely replicate that look by customizing an already made theme, or building a theme of your own from scratch.
When I want to customize a theme, I usually start with a totally blank canvas theme (like Starkers by Elliott Jay Stocks ). That gives me maximum control over what I want to put on the page.
Of course, I'm good with HTML/CSS/PHP. If you're not, you may want to follow along with a tutorial on how to customize a wordpress theme. There's a great one that can be found at the ThemeForest Blog called WordPress for Designers. Tuts+ also has some nice WordPress theme development tutorials that take you from looking at a layered photoshop file, all the way through a live theme.
If you don't want to go through all of that, you can also just edit a standard theme to your liking. That is best done by replacing the requisite images, and altering the theme's stylesheets to suit your needs.
Regardless of how you go about it, you should be able to use your headers, banners, backgrounds, and whatever else you need/want.