What's the right way of getting category list of a Wordpress web site using PHP?

I need to read the list of Wordpress categories of a blog and insert them as hyperlinks into my PHP Page. I used simplexml_load_file and it's working on my local Wamp Server perfectly. But I'm worried about performance of the production server with a lot of users. Should I do caching for production page? How? Is there another standard solution for this?

$feed_url = "http://my.web.site/category/$category/feed/";

// If there is some errors, return empty
if(! $news_xml = @simplexml_load_file($feed_url, 'SimpleXMLElement', LIBXML_NOCDATA & LIBXML_NOWARNING & LIBXML_NOERROR))
{
    log_message('error','Feed load error: '.$feed_url);
    return [];
}

$data = [];

foreach ($news_xml->channel->item as $news_item) {
    $new_item = [
        "title" => (string)$news_item->title,
        "link" => (string)$news_item->link,
        "comments" => (string)$news_item->comments,
        "pubDate" => (string)$news_item->pubDate,
        "category" => (string)$news_item->category,
        "guid" => (string)$news_item->guid,
        "description" => (string)$news_item->description,
    ];
    if ($news_item->children('media', true)->content) {
        $new_item["image_url"] = (string)$news_item->children('media', true)->content->attributes()->url;
    }

    $data[] = $new_item;
}