get_the_category, limited and by ID

I’m currently grabbing the first category for a post by the following method:

<?php
$category = get_the_category();
if($category[0]){
echo '<a class="entry-category" href="'.get_category_link($category[0]->term_id ).'">'.$category[0]->cat_name.'</a>';
}
?>

This is working perfectly, BUT we want to exclude a category and its children from display.

First thought was to exclude by an array of IDs, but get_the_category doesn’t allow that.

Second thought was to change the category IDs, so that the “first” category the code came up with would be the one we wanted. Would take a bit of fudging, but would do the job. However, get_the_category returns an alphabetised list rather than by cat ID.

Would love to know how one can return:
– only one category.
– excluding some categories (by either exclusion method above).
– linked up and formatted as above.