How can I style my theme admin page?

In your construct function you also need to enqueue a custom stylesheet that will house the CSS to style up your theme options.

A simplified example would look like this:

function admin_style() {
    wp_enqueue_style( 'theme-options-style', get_template_directory_uri().'styles/theme-options-style.css');
}
add_action('admin_enqueue_scripts', 'admin_style');