wp_head() not inserting the default stylesheet style.css

Actually you shouldn’t add JS and CSS files to your header.php, but make use of the functions wp_enqueue_script() and wp_enqueue_style() to add them there.

Example taken from the codex page:

/**
 * Proper way to enqueue scripts and styles
 */
function theme_name_scripts() {
    wp_enqueue_style( 'style-name', get_stylesheet_uri() );
    wp_enqueue_script( 'script-name', get_template_directory_uri() . '/js/example.js', array(), '1.0.0', true );
}

add_action( 'wp_enqueue_scripts', 'theme_name_scripts' );