How to get one result using wpdb class?

You’ve made no attempt to check for errors, e.g. $result may be false, also your code would fail if there was more than one result returned.

So instead of using a custom table, and reinventing the wheel, use the provided APIs:

get_theme_mod and set_theme_mod

So your code now becomes:

function asec_get_link_color( $default_color="blue") {
    return get_theme_mod( 'link-color', $default_color );
}

Using set_theme_mod also handles all your SQL escaping and security code for you.

Also keep in mind that you use wp_theme_options as your table name, but you’re not the only person building themes. At the very least, add an identifier unique to your theme and yourself.