Igorsrt,
может вы это хотели?
<!DOCTYPE HTML>
<html>
<head>
<title>Untitled</title>
<meta charset="utf-8">
<style type="text/css">
.selected {
background-color: #FF00FF;
}
</style>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.0/jquery.min.js"></script>
<script>
$(function(){
$('input.shipping_method').click(function() {
$('li.shipping_method').each(function(indx, element){
if ($('input',this)[0].checked) {
$(this).addClass('selected');
} else {
$(this).removeClass('selected');
} });
}).filter(":checked").click();
})
</script>
</head>
<body>
<ul>
<li class="shipping_method">
<input type="radio" name="shipping_method[0]" data-index="0" id="shipping_method_0_flat_rate" value="flat_rate" class="shipping_method" checked="checked"><label for="shipping_method_0_flat_rate">Доставка1</label><div style="float:right;">300 руб.</div></li>
<li class="shipping_method">
<input type="radio" name="shipping_method[0]" data-index="0" id="shipping_method_0_local_delivery" value="local_delivery" class="shipping_method"><label for="shipping_method_0_local_delivery">Доставка2</label><div style="float:right;">500 руб.</div></li>
</ul>
</body>
</html>