A different CSS for front page

if your theme uses body_class() http://codex.wordpress.org/Function_Reference/body_class in the body tag, you will have a specific css class for the front page (.home), which you could use in the stylesheet;

example (might be different for your theme):
.home #content .entry { color: #123edf; }

to overwerite the genral stylesheet style.css, you could use a conditional statement in header.php to link a specific stylesheet for the front page:

example:

<?php if( is_home() ) { ?>
<link rel="stylesheet" type="text/css" media="all" href="<?php echo get_stylesheet_directory_uri(); ?>/front-style.css" />
<?php } ?>

the code needs to be after the link to the general stylesheet.

(instead of is_home() you might need to use is_front_page() )
http://codex.wordpress.org/Conditional_Tags
http://codex.wordpress.org/Function_Reference/get_stylesheet_directory_uri

—
alternative, to load a different stylesheet instead of the general stylesheet, use the conditional statement with an ‘else’:
(this code would replace the link of the general stylesheet)
example:

<?php if( is_home() ) { ?>
<link rel="stylesheet" type="text/css" media="all" href="<?php echo get_stylesheet_directory_uri(); ?>/front-style.css" />
<?php } else { ?>
<link rel="stylesheet" type="text/css" media="all" href="<?php bloginfo( 'stylesheet_url' ); ?>" />
<?php } ?>

alchymyth,

Thanks for the detailed post. I used the pure css .home solution you provided to get rid of the padding on my homepage, but keep it on the others by adding this:

.hentry {padding: 0 25px; }
.home .hentry {padding: 0; }

As you’re not contributing to the original poster, you should create your own thread on the issue.