Woocommerce have many shipping methods. If you want to select the cheapest shipping method for your customer then add the below given code in your functions.php

add_filter( 'woocommerce_package_rates' , 'cheapest_woocommerce_shipping_method', 10, 2 );
function cheapest_woocommerce_shipping_method( $rates, $package ) {
	if ( ! $rates ) {
		return;
	}

	$prices = array();
	foreach( $rates as $rate ) {
		$prices[] = $rate->cost;
	}
	
	array_multisort( $prices, $rates );
	
	return $rates;
}