Wordpress - How can I version the main CSS file?

This may be inappropriate, please let me know if I missed something.

The fourth argument to wp_enqueue_style() is the stylesheet's version number. In your theme's functions.php:

function my_theme_styles() {
    // replace "10" with your version number; increment as you push changes
    wp_enqueue_style('my-theme-style', get_bloginfo('template_directory') . '/style.css', false, 10);
}
add_action('wp_print_styles', 'my_theme_styles');

Requires that your header.php does a wp_head(), which of course you were doing anyway. ;)

This allows you to push long expiry headers with your CSS file, and force clients to download a new file by updating the version number. WP will append "?ver=N" to the URL of your CSS file.

Drop this in your theme's functions.php file:

function my_cool_style_versioner( $style ){
  return str_replace( '/style.css', '/style-1.css', $style );
}

add_filter( 'stylesheet_uri', 'my_cool_style_versioner' );

Style.css is required for your WordPress theme. That's where WordPress gets the theme name and meta information for the Appearance >> Themes menu from. That said, you don't actually have to use style.css in your theme at all. I know of several readily available themes that don't use it, and I only use it in a handful of my custom designs.

In header.php just place the following tag in place of the regular stylesheet link:

<link rel="stylesheet" type="text/css" href="<?php bloginfo('stylesheet_directory'); ?>/style-1.css" />

This will load your alternative stylesheet as the page's stylesheet and completely ignore the regular style.css.