Magento – Find out to which categories a product belongs to

Okay, so have actually got quite a decent solution to this now using my second approach in my question. I'm unsure of the performance implications as of yet but here is what I have done...

<?php $categories = $_product->getCategoryIds(); ?>
<?php foreach($categories as $k => $_category_id): ?>
<?php $_category = Mage::getModel('catalog/category')->load($_category_id) ?>
<?php $ignoredcats = array(2,360,124,4); ?> <!-- add all category ID's here that we wish to ignore -->
    <?php if (in_array($_category_id, $ignoredcats )){ ?>
        <?php //do nothing ?>
<?php } else { ?>
<?php if($_category->getIsActive()): ?> <!-- make sure the category is active first -->
    <p>View more <a href="<?php echo $_category->getUrl() ?>/filter/<?php echo strtolower ($manufacturerName = $_product->getAttributeText('manufacturer')) ?>" onclick="_gaq.push(['_trackEvent', 'Internal Linkage', 'Product Back To Links', '<?php echo $manufacturerName = $_product->getAttributeText('manufacturer') ?> <?php echo $_category->getName() ?>',, false]);"><?php echo $manufacturerName = $_product->getAttributeText('manufacturer') ?> <?php echo $_category->getName() ?></a> from Showermania.</p>
<?php endif; ?>

This will then output something like the following screenshot shows but by specifying the category ID's in $ignoredcats will only render for the categories of my choice.

I can then style or modify the output accordingly. You could alternatively only output this for allowed categories instead of else not allowed instead if wanted.

Does the job effectively for me currently but yet to notice any performance implications or any issues that will arise from this.

You can use following code to avoid parent categories.

<?php
    $catIds=$_product->getCategoryIds();
    $Category=Mage::getSingleton('catalog/category')->getCollection()
                    ->addAttributeToFilter('entity_id', $catIds)
                    ->addAttributeToFilter('level', array('gt'=>0));

    foreach($Category as $child):
        if($child->hasData()):              
?>
            <a class="" href="<?php echo Mage::helper('core/url')->getHomeUrl().$child->getRequestPath().DS ?>">
                <li class="level3">                         
                    <span><?php echo $child->getName() ?></span>
                </li>               
            </a>
<?php
        endif;
    endforeach;             
?>

you can use level attribute filter to get child categories. Now in my code I am avoiding only the parent level categories only.