WP_query for links?

I’m looking to make a list of three random links for my site. I have worked with the wp_list_bookmarks() function and done everything possible with it but have found that it is impossible to style my links like I would like to.

I’m wondering if any of you know a way to query for WordPress links like you would normally with PHP or using the WP_query?

I was trying something like this:

<?php
$my_query = new WP_query('SELECT link_url, link_name, link_target, link_description FROM wp_links WHERE link_visible="Y" ORDER BY RAND() LIMIT 3');

// I believe my problem is here... I don't know how to capture the queried data in variables...
	$name = $post->link_name;
	$url = $post->link_url;
	$target = $post->link_target;
	$description = $post->link_description;

	$description = cropsentencepost($description, 200, "...", $name, ' - ');

	echo "	<div class=\"link\"><a href=\"$url\" target=\"$target\">$name</a><small> - $description</small></div>\n";

wp_reset_query();
 ?>

This could be way off, but it at least doesn’t give my any error messages. It just doesn’t display the data.

Thanks in advance, any help is really appreciated!