How to invoke a HTML custom button based on a HTML dropdownlist menu

You want to use admin-post.php or admin-ajax.php (AJAX only) to allow your front-end form to interact with WordPress.

Setting this up will allow you to create an action where you use the $_POST array to find the content you’re looking for with WP_Query and print it out as the response to your request.

Here’s a decent guide to both methods: