I want to create a page in Magento that shows a visual representation of the categories.. example
CATEGORY
product 1
product 2
ANOTHER CATEGORY
product 3
From code found in an SEO related class (Mage_Catalog_Block_Seo_Sitemap_Category)
$helper = Mage::helper('catalog/category');
$collection = $helper->getStoreCategories('name', true, false);
$array = $helper->getStoreCategories('name', false, false);
Try to forget that it's a database that's powering your store, and instead concentrate on using the objects that the Magento system provides.
For example, I had no no idea how to get a list of categories. However, I grepped through the Mage codebase with
grep -i -r -E 'class.+?category'
Which returned a list of around 30 classes. Scrolling through those, it was relatively easy to guess which objects might have methods or need to make method calls that would grab the categories.