Welcome to Sitepoint
That Wordpress theme is adding a 'home' class to the body tag.
If you view source on a page it will have:
You can add custom styles in Wordpress in Appearance > Editor > Styles
<body class="home page page-id-12 page-template-default custom-background">
If you are happy with how the background is showing now you can add these below, and remove it from where you currently added it to all pages.
You can use the same class hook to move the menu if you want.
background: url("http://athrill.co.uk/wp-content/uploads/2012/03/hunta1.jpg") scroll center top no-repeat;
For more serious changes to layout you may need to use a different template for the home page so you can have different HTML as well.
All the best,