StartGames,
<!DOCTYPE html>
<html>
<head>
<title>Untitled</title>
<meta charset="utf-8">
<style type="text/css">
.radio-input.active {color:red !important}
</style>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
<script>
$(function() {
$('#shipping_method_list').on('change','[name="shipping_method"]', function() {
$(this).parents('div.radio-input').addClass('active').siblings('div.radio-input').removeClass('active');
});
});
</script>
</head>
<body>
<div id="shipping_method_list">
<strong class="title nn">Доставка</strong>
<div class="radio-input radio active" id="su.flat.flat">
<label for="flat.flat">
<input type="radio" name="shipping_method" value="flat.flat" id="flat.flat" checked="checked" data-refresh="5" class="styled">
<span class="text">Доставка</span><span class="price">80 руб</span></label>
</div>
<strong class="title nn">Самовывоз</strong>
<div class="radio-input radio" id="su.pickup.pickup">
<label for="pickup.pickup">
<input type="radio" name="shipping_method" value="pickup.pickup" id="pickup.pickup" data-refresh="5" class="styled">
<span class="text">Самовывоз</span><span class="price">0 руб</span></label>
</div>
</div>
</body>
</html>