How do I control which e-mails I recieve?

This cannot be based on price, but since free orders are completed right away you can unhook that part:

add_action( 'woocommerce_email', 'remove_some_emails' ); 

function remove_some_emails() {
remove_action( 'woocommerce_order_status_pending_to_completed_notification', array( WC()->mailer()->emails['WC_Email_New_Order'], 'trigger' ) );
}